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Merz, John Theodore, 1840-1922. 

A history of Euiopean thought in the nineteenth century, 
by John Theodore Merz ... Edinburgh and London, W. 
Blackwood and sons, 4003-14: If '07-14. 

4 V. 21 cm. 

Vol. 1 :;2<I unaltered edition, i»04: 1^'07 . 

Contents. — pt. I. Scientific thought. 2 v. — pt. II. Philosophical 
thought, 2 V. 

Copy in bur{;:or3S.--1907-14.— 4 V. 

1. rhilosophy, Modern-4ji8tT 2. Science— Hist. i. Title. 




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As the plan of this work is fully given in the Introduction, 
only a few points, chiefly of a personal character, remain to 
be touched on here. 

The first refers to the motive which led me to a course 
of studies, extending over more than thirty years, of which 
this book is the outcome. 

The object of the book is philosophical, in the sense now 
accepted by many and by divergent schools — i.e., it desires 
to contribute something towards a unification of thought. 
When ito the beginning of my philosophical studies I be- 
came convinced that this is the task of philosophy, I felt 
the necessity of making myself acquainted, at first hand, 
with the many trains of reasoning by which, in the 
separate domains of science, of practical and of individual 
thought, such a unification has been partially and success- 
fully attempted. Such a survey seemed to me indispens- 
able. The possession of a map showing the many lines of 
thought which our age has cultivated seemed to me the 
first requisite, the basis from which a more complete 



unification would have to start. The following pages 
contain the result of this survey. Like every survey, it 
can claim to be merely an approximation. It gives outlines 
which closer scrutiny will have to correct and fill up. 

My original intention was to complete this survey in 
three volumes, corresponding to the three divisions of the 
subject set out in the Introduction. 

Some of my friends, who desired that the publication 
of the book should not be unduly delayed, considered that 
the Introduction and the earlier chapters of the work would 
give something intelligible in themselves, and urged the 
advantage of smaller volumed. I therefore decided to com- 
plete the first part of the history, which deals with scientific 
thought, in two volumes instead of in one. 

For the information of my readers, I mention here that: 
the two last chapters of this volume, which treat of thq 
astronomical and of the atomic views of Nature, will b( 
followed in the second volume by similar chapters oi 
the mechanical, the physical, the biological, the statistical^ 
and the psychophysical views of Nature, and that it is m; 
intention to close the first part of my subject by an attempt 
to trace concisely the development of mathematical thought 
in this century. 

My thanks are due to many friends who have supported 
me with assistance and encouragement. 

I consider myself fortunate in having secured for the 
revision of the whole volume the invaluable aid of Mi 
Thomas Whittaker, B.A., whose profound erudition, know- 




ledge of ancient and modern literature, and great editorial 
experience, were well known to my late friend Professor 
Groom Eobertson, during his successful editorship of the 
first series of 'Mind,* 

Mr S. Oliver Eoberts, M.A., of the Merchant Taylors' 
School, has kindly read over the fourth, and Professor 
Phillips Bedson, of the Durham College of Science of this 
city, the last, chapter of this volume. The Introduction has 
greatly benefited by a thorough revision by my brother- 
in-law, Dr Spence Watson, a master of the English language. 

I must also thank him and Dr Thomas Hodgkin for 
having given me what I value as much as assistance— 
namely, encouragement. 

One indeed to whom I am in this respect more indebted, 
perhaps, than to any one else — whom to have known has 
meant, for many, a revelation of the power of mind and 
the reality of spirit — is no more: Ernst Curtius. While 
I was writing the last pages of this volume, in which he 
took a warm interest, the tidings arrived that he had passed 
away. But she who was nearest and dearest to him is 
still with us — a true priestess of the higher life, who has 
kept burning in the soul of many a youthful friend the 
spiritual fire when it was in danger of being quenched by 
the growing materialism of our age. 


The Quarries, 
Newcastle-upon-Tyne, November 1896. 





I. Thought, the hidden world, 1 ; The only moving principle, 2 ; History of 
Nature, how to be understood, 2 ; Not intelligible without intellect, 2 ; 
History of savage tribes, what is it ? 3 ; Two ways in which thought enters 
into history, 4 : Definition of thought impossible, 4 ; Relation of outer 
and inner worlds undefined, 5 ; Many meanings of thought, 5 ; Thought 
of the present age, 6 ; Contemporary history, to what extent possible 
and valuable, 6 ; Supposed objectivity of historians, 7 ; Value of contem- 
porary records, 8 ; Mystery of the life of thought, 8 ; Latent thought the 
material for genius, 8 ; Contemporary record of thought more faithful, 
10 ; Events of the immediate past, 10 ; Changes of language, 11 ; Coining 
of new words, 12 ; Object of this work, 13 ; Not a political history, nor a 
history of science, literature, and art, 13 ; Influences which have a result 
on our inner life, 14 ; Personal knowledge necessary, 14 ; American influ- 
ence only touched upon, 14 ; Only French, German, and English thought 
treated, 15 ; Unity of thought, a product of this century, 16 ; Voltaire, 
16; Adam Smith, 16; Coleridge and Wordsworth, 17; Mme. de Stael, 
17 ; rtiris the focus of science, 17 ; Babbage, Herschel, and Peacock, 18 ; 
Liebig's laboratory, 18 ; Comte's philosophy, 18 ; Constable's influence in 
France, 19 ; Science become international, 19 ; The light which etymology 
throws on the history of thought, 20 ; Goethe, 22 ; Peculiarity of the 
German language, 22 ; New thought has found new words, 23 ; De Bon- 
ald and Max Miiller, 23 ; Thought, how expressed in French and Ger- 
man, 24 ; Philosophy of history, 25 ; Want of precise terms in German 
and French, 26 ; Carlyle, 26. 






II. The two factors of intellectual progress, 27 ; Object of the book, 28 ; 

Nineteenth century, what it has achieved : (a) Method of knowledge ; (6) 
Unity of knowledge, 29 ; Search after truth, 29 ; Method of science, prac- 
tised by Galileo, &c., defined by Bacon, &c., 30 ; Disintegration of learn- 
ing, 30 ; Apparent distance between science and poetry, 31 ; Closer con- 
nection between science and Ufe, 31 ; What has nineteenth century done 
for the ideals ? 32 ; Deeper conception of the unity of human interests, 
33 ; Dififerent terms for expressing this unity, 33 ; Definition of thought, 
33 ; Age of encyclopaedic treatment of learning, 34 ; Unity of knowledge 
gradually lost sight of, 35 ; Lectures on " Encyclopadie " in Germany, 37 ; 
Encyclop£edias did not fulfil their promise, 39 ; French were masters in 
science in beginning of the century, 41 ; Reaction in Germany against 
metaphysics, 43 ; Reform in school literature, 44 ; Germany has taken 
the lead in studying the life of thought, 46 ; Transition from meta- 
physical to historical method, 47 ; Herbert Spencer, 48 ; Lotze, 48 ; 
Herder's *Ideen,' 50; Humboldt's * Kosmos,' 51 ; Lotze's ' Microcosmus,' 
52 ; What the mental life of mankind consists of, 55 ; Methods have 
their day and cease to be, 56. 

III. Necessity of choosing a road, 57 ; No central event in our age, 58 ; Is 
history of thought historj- of philosophy ? 60 ; Goethe's work involves 
the deepest thought of the century, 61 ; Philosophy retrospective, 62 ; 
Two questions, 63 ; Speculation, 64 ; Philosophy defined, 65 ; Division 
of the book, 65 ; Neither science nor philosophy exhausts " thought," 66 ; 
Thought also hidden in literature and art, 66 ; Goethe's and Words- 
worth's influence, 67 ; Unmethodical thought, 68 ; Summed up in term 
"religious thought," 69 ; Science is exact, 69 ; Subjective interests, 70 ; 
Philosophy intermediate between exact science and religion, 71 ; Three- 
fold aspect of thought : scientific, philosophical, individual, 72 ; Difficult 
to separate the three aspects, 74 ; French thought centred in science, 
75 ; State of philosophy in England, 75 ; Goethe's ' Faust' representative 
of the thought of the century, 76 ; A period of ferment, 76 : Caused by 
the Revolution, 77 ; Thought of century partly radical, partly reactionary, 
77 ; Byronic school, 78 ; Revolutionary theories, 79 ; Thought to be con- 
sidered as a constructive power, 80 ; Darwin, Spencer, and Lotze, ^1 ; 
Romanticism, 82 ; Scientific thought to be dealt with first, 84 ; Hegel's 
doctrine, 85. 

t [ 



Three chapters on the growth and the diffusion of the scientific spirit 
in the first half of the nineteenth century. 



Our century the scientific century, 89 ; Difference of English and Continental 
notions of science, 91 ; Relation of science and life, 92 ; Foreseen by 
Bacon, 93 ; Defect in Bacon's Philosophy, 94 ; Corrected by Newton, 95 ; 
Bacon's and Newton's ideas taken up by French philosophers : Bacon and 
Newton compared, 96 ; Laplace's work, 97 ; French Academy of Sciences, 
99 ; Continental methods in mathematics, 100 ; Modern analytical 
methods, 102; Older synthetical methods, 103; Influence of science 
on French literature, 104 ; Absence of this influence in England and 
Germany, 106 ; Schools of science in Paris, 106 ; Promoted by Govern- 
ments of Revolution, 108 ; Condorcet, 110 ; Lakanal, 111 ; Ecole normale, 
Ecole poly technique, 112 ; Monge's 'Descriptive Geometry,' 114 ; Science 
of Chemistry, 114 ; New mathematical sciences, 116 ; Crystallography, 
116 ; Theory of probability, 118 ; Laplace^^ned his results by dis- 
regarding "individuality," 124 ; The centre of interest in the sciences of 
life, 125 ; Into this centre Cuvier carried exact research, 128 ; Cuvier's 
training, 133 ; Cuvier the greatest representative of the Academic system, 
136 ; Science during the Revolution and First Empire, 138 ; Popular- 
isation of science in France, 142 ; Literary and national popularisation, 
142 ; Dangers of the former, 143 ; The Revolution added the practical 
popularisation, 145; Influence of the first Napoleon on science, 149; 
Napoleon favoured the mathematical sciences, 151 ; Discountenanced 
contemporary philosophy, 152 ; Used statistical methods, 153 ; Promi- 
nence given deservedly to French names by Cuvier, 155. 



Foundation of German universities, 158 ; Development of the universities by 
the people, 159 ; Geographical distribution of the universities, 162 ; Full 
development of the German university system, 163 ; Philosophical fac- 
ulty, 164 ; University of Gottingen, 164 ; Relation of universities and 

'>■ ■: 

• f 



high schools, 166 ; The university a training-school for research, 167 ; 
The ideal of Wissenschaft, 168 ; Developed under the German university 
system, 170 ; Reception of exact science in Germany, 174 ; Science not 
yet domiciled during the eighteenth century, 178 ; Scientific periodicals, 
180 ; Gauss's mathematical researches, 181 ; Scientific spirit enters the 
universities in second quarter of century, 183 ; Jacobi's mathematical 
school, 185 ; Chemical laboratories established in 1826 through Liebig, 
188 ; Cosmopolitan character of German science, 189 ; Liebig's organic 
analysis, 191; Biology a German science, 193; Cellular theory of 
Schleiden, 194 ; and Schwann, 195 ; Ernst Heinrich Weber, 196 ; and 
Johannes MilUer, 197 ; Psychophysics, 198 ; Spirit of exact research and 
Wissenschaft, 202; Encyclopaedic view necessary in philosophy and 
history, 203 ; Philosophy of Nature, 204 ; Conflict between the scientific 
and the philosophical views, 205 ; A. von Humboldt, 206 ; Influence of 
Berzelius on German science, 208 ; Philosophy of Nature and medical 
science, 209 ; Science for its own sake, 211 ; Bequest of the classical and 
philosophical school, 211 ; Completeness and thoroughness of research, 
213 ; Combination of research and teaching, 214 ; Combination of science 
and philosophy, 215 ; Biology grown out of science and philosophy com- 
bmed, 216 ; Du Bois-Reymond on Miiller, 217 ; "Vital force" abandoned, 
218 ; Mechanical view in biology, 219 ; Criticism of principles of mathe- 
matics, 221 ; The exact, the historical, and the critical habits of thought, 



Scientific organisation abroad, 226 ; Similar institutions in Great Britain, 227 ; 

English science in the early part of the century, 229 ; Alleged decline of 

science in England, 230 ; Criticisms of Playfair, 231 ; Babbage's criti- 

cisms, 233 ; Foreign opinions on English science, 235 ; English repUes to 

Babbage, 238 ; Foundation of the British Association, 238 ; Character- 

istics of higher mental work in England, 239 ; Academies and universities 

not always impartial, 240; Fourier, 241; Fresnel, 241; Plucker, 

242 ; Grassmann, 243 ; Central organisation wanting in England, 243 ; 

Thomas Young, 244 ; Dalton, 245 ; Faraday, 246 ; Green, 246 ; Boole, 

247 ; Babbage, 248 ; Characteristics of English thought, 249 ; Absence of 

schools of scientific thought, 250 ; Individual charact^->aud practical 

tendency of English science, 251^; English peculiarities more pronounced 

during earlier part of the c'St'ury, 252 ; Unique character of English 

universities, 254 ; Ideal of ''liberal education," 255 ; Union of education 

and instruction, 258 ; Educational organisations in England, 262 ; The 





Royal Institution, 264 ; Manchester Literary and Philosophical Society, 
265 ; John Dawson of Sedbergh, 267 ; The Scotch Universities, 267 ; The 
Royal Society of Edinburgh, 269; The 'Edinburgh Review,' 270; The 
Analytical Society of Cambridge, 271 ; University life in Scotland, 271 ; 
The Dublin Mathematical School, 274 ; Importance of British contribu' 
tions to science, 276 ; Difiusion of scientific knowledge on the Continent, 
276 ; Isolation of English men of science, 277 ; Individualism of the 
English character, 279j Changes during the last fifty years, 280 ; British 
contributions to biology, 282 ; Jenner, 284 ; English love of nature, 2S4^ 
Union of individualism and naturalism in England, 286; White of Sel- 
bome, 288 ; The Geological Society, 290 ; William Smith, 291 ; Charles 
Bell, 292 ; Historical Geography, 294 ; Martin William Leake, 296 ; Work 
of the three nations compared, 298. 



The scientific spirit in the first and second half of the century, 302 ; Science 
become international, 303 ; Disappearance of national differences, 305 ; 
Special scientific ideas, 306; Philosophy of science, 306; Whewell's 
'History' and 'Philosophy,' 309 ; Philosophy and science, 311 ; Leading 
scientific ideas mostly very ancient, 312 ; Mathematical spirit, 314 ; 
When first introduced into science, 317 ; Newton's 'Principia,' 318 ; The 
gravitation formula, 319; Lines of thought emanating from it, 321 ; 
Element of error, 323 ; Laplace and Newton, 326 ; Several interests 
which promote science, 326 ; Insufficiency of observation, 328 ; Practical 
interest, 328 ; Focalising effect of mathematical formula, 332 ; Matter 
and force mathematically defined, 334 ; Weight and mass, 336 ; Gravi- 
tation not an ultimate property of matter, 338 ; Attraction and repulsion, 
342 ; Electrical and magnetic action, 344 ; Law of emanations, 344 ; 
Molecular action, 346 ; The astronomical view : Cosmical, molar, and 
molecular phenomena, 348 ; Special interest attached to molar dimen- 
sions, 350 ; Geometrical axioms, 352 ; Difficulty of measuring gravitation 
directly, 353 ; Astronomical view of molecular phenomena, 354 ; Capil- 
lary attraction, 356 ; Boscovich's extension of the Newtonian formula, 
357 ; Coulomb's measurements, 360 ; Extended by Gauss and Weber, 
360 ; Davy and Faraday, 363 ; Ampere and Weber develop the astro- 
nomical view, 366 ; Weber's fundamental measurements, 368 ; Necessity 
of developing the infinitesimal methods, 373 ; Newtonian formula the 
basis of physical astronomy, 375 ; The Newtonian formula unique as to 
universaHty and accuracy, 377; Is it an ultimate law? 378; Laplace's 
opinion, 378 ; Opposition to the astronomical view of nature, 381. 








Recapitulation, 382 ; Atomic theory, 385 ; Lavoisier, 386 ; Phlogistic theory, 
388 ; Theory of combustion, 389 ; Rule of fixed proportions, 392 ; J. 
Benjamin Richter, 393 ; Dalton, 394 ; Berzelius, 396 ; Atomic theory 
and gravitation compared, 396 ; WoUaston's prophecy, 397 ; Rule of 
multiple proportions, 398; Equivalents, 399; ** Simplex sigillum veri," 
401 ; Prout's hypothesis, 402 ; Discovery of Isomerism, 405 ; Organic 
Chemistry, 407 ; Liebig's definition of same, 409 ; Type theory, 411 ; 
Uncertainty in chemical theory about middle of century, 413 ; Two 
aspects of the atomic theory, 415 ; A convenient symbolism, 417 ; 
Neglect of the study of affinity, 420; Kopp on chemical theory in 1873, 
421 ; The periodic law, 422 ; Difference between chemical and physical 
reasoning, 424 ; The kinetic theory of gases, 425 ; Avogadro's hypothesis, 
427 ; Neglect of same, 429 ; Development of the atomic view, 431 ; 
Pasteur's discovery of '* Chirality," 431; Atom and molecule, 432; 
Joule's calculations, 434 ; Clausius's first memoir, 435 ; Internal energy 
of molecules, 436; The atomic theory accepted as a physical theory 
about 1860, 437 ; Clerk Maxwell : The statistical view of nature, 438 ; 
Doctrine of averages, 440 ; Geometrical arrangement of atoms, 441 ; 
Crystallography, 441 ; Analogy between crystallographic and atomic 
laws, 444 ; Isomorphism, 444 ; Polymorphism, 446 ; Structural and 
stereo-chemistry, 447 ; Valency, 447 ; Atomic linkage, 449 ; The carbon 
tetrahedron, 450 ; Defects and insufficiency of the atomic view, 451 ; 
Theories of chemical affinity, 452 ; Practical influences, 453 ; Change in 
definition of organic chemistry, 454 ; Criticisms of the atomic view, 455. 




Behind the panorama of external events and changes i. 
which history unfolds before our view there lies the S^e^Si'^ 
hidden world of desires and motives, of passions and "'"■ 
energies, which produced or accompanied them ; behind 
the busy scenes of Life lie the inner regions of Thought. 
Only when facts and events cease to be unconnected, 
when they appear to us linked together according to' 
some design and purpose, leading us back to some 
ongmating cause or forward to some defined end, can 
we speak of History in the sense which the word has 
acquired in modern language; and similarly do the 
hidden motives, desires, and energies which underlie or 
accompany the external events require to be somehow 
connected, to present themselves in some order and con- 
tinuity, before we are able to grasp and record them. 

VOL. I. 




the only 


History of 
Nature, how 
to be under- 


Not intelli- 
gible with- 
out intel- 


That which has made facts and events capable of being 
chronicled and reviewed, that which underlies and con- 
nects them, that which must be reproduced by the his- 
torian who unfolds them to us, is the hidden element of 
Thought. Thought, and thought alone, be it as a principle 
of action or as the medium of after-contemplation, is 
capable of arranging and connecting, of combining what 
is isolated, of moving that which is stagnant, of propel- 
ling that which is stationary. Take away thought, and 
monotony becomes the order. 

This assertion may seem bold to many, who would look 
rather to the gra^d phenomena of Nature than to the 
narrow limits of man's activity. A few remarks will, 
however, suffice to show that my proposition is not 
opposed to the view which they take. It may be 
urged that, independent of human life altogether, the 
earth has a history, the planetary system has a develop- 
ment, and that, according to modern theories, evolution 
is the principle which governs inanimate as well as ani- 
mated nature; that rest and sameness are nowhere to 
be found, everywhere change and unrest. But change 
and unrest do not necessarily constitute history. Motion 
and change would be as monotonous as absolute rest, 
were they merely to repeat themselves endlessly, did the 
whole movement not produce something more, and were 
this something more not greater or better than the 
beginning. But greater and better are terms which imply 
comparison by a thinking beholder, who attaches to one 
thing a greater value than to another, judging by certain 
ideal standards, which are not in the objects or process of 
nature themselves, but are contained only in his own think- 




ing mind. It may be that a mechanical and mindless series 
of changes can produce numbers without end, or forms of 
countless variety: but this process would deserve the name 
of history only if either the transition from unity to mul- 
tiplicity, or the production of formal variety, were capable 
of being understood by a thinking mind,— if the result 
of the process were a matter of some concern, if an 
interest were attached to it, if a gain or loss could be 
recorded. The pendulum which swings backwards and 
forwards in endless monotony, the planet which moves 
round the sun in unceasing repetition, the atom of matter 
which vibrates in the same path, have for us no interest 
beyond the mathematical formute which govern their 
motions, and which permit us mentally to reproduce, i.e., 
to think them. A combination of an infinite number of 
these elementary movements would have as little interest, 
were it not that out of such a combination there resulted 
something novel and unforeseen: something that wa^ 
beautiful to behold or useful to possess, something that 
was valuable to a thinking mind in a higher or lower 
meaning of the word. 

But if, even in inanimate nature, the processes of change 
acquire an interest, possess a history, only if referred to 
a thinking mind which can record, understand, and appre- 
ciate them, how much more is this the case when we deal 
with human affairs, where man is not only the thinking 
beholder but the principal agent ? Here the historic 
interest would cease, were the succeeding years and ages 
to produce no valuable change, were the rule of existence 
and the order of life to repeat themselves in unceasing ™'^^<" 
monotony. The savage tribes of Africa have a history: but L"^^' """ 


Two ways 
in which 
enters into 

of Thought 


this history is all known when the order of the day, the 
year, at most of a generation, is known. Even the highly 
complicated but stagnant life of China would have a short 
historical record — many thousands of years taking up no 
more space than as many days of modern European history: 

"Better fifty years of Europe than a cycle of Cathay." 
Thus it is that Thought becomes in two ways a subject 
of great interest and importance to the historian. Of 
every change in nature or human life we can ask : What 
has been its result in the world of thought? What 
gain or loss, what progress, has it worked in the minds 
of men, of us the beholders? Has it increased our 
knowledge, enriched our stock of ideas, deepened our 
insight, broadened our views and sympathies— in one 
word, has it added to our interests ? has it made larger 
and fuller our inner life ? 

And of every change in human affairs we can ask this 
further question : What part has thought, the inner life, 
played in this change ? These two questions mark the 
task of the historian of Thought. 

I do not think it necessary or practicable at this stage 
to explain minutely the terms with which we have so 
far been dealing. Many a one might be tempted to ask 
for a definition of Thought, or for a preciser statement of 
the actual relation between Nature, Life, and Thought.^ 

1 In refusing to define what I 
mean by Thought, I take up the 
opposite position to that occupied 
by Prof. Max Miiller in his latest 
work, 'The Science of Thought,' 
London, 1887, p. 1, where he says : 
" I mean by Thought the act of 
thinking, and by thinking I mean 

no more than combining. I do 
not pretend that others have not 
the right of using Thought in any 
sense which they prefer, provided 
only that they will clearly define 
it." So far as definition is at all a 
part of the work of the historian, 
I maintain that it is the result and 


Such definitions must be left to the reader himself, if 
in course of the perusal of these volumes he finds' it 
necessary to form abstract theories on these points. 
Any definition given now would inevitably involve us in 
controversies, which would be embarrassing and con- 
fusing. I rely upon the general and undefined sense of 
the word Thought, assuming that every one will connect 
some intelligible meaning with it, some meaning which 
will enable him to understand the very general pro- 
position with which we started, the existence of an 
inner or hidden world behind the world of external 
events and facts, the continually changing nature of 
this inner world, and the connection and reaction be- 
tween the two worlds. Whether in time and in im- 
portance the outer or the inner world is the first, 
whether within the latter equal value attaches to thJ 
clearer province of Eeason, i.e., defined Thought, to the 
obscurer regions of Feeling and Imagination, and to the 
unconscious world of Impulse, these are questions which 
it is not necessary to answer at present. As it was 
enough to point to the existence of the two worlds of 
Life and Thought, so it will be enough to notice that 
thought does not mean merely defined, clear, methodical 
thought, but likewise the great region of desire, impulse, 
feeling, and imagination, all of which play, we must 
admit, a great part in the inner life of the soul as well 
as in that of the outer world. 

Relation of 
outer and 
inner world 



Many mean* 
ings of 

outcome of his narrative, the im- 
pression which he leaves on the 
mind of the reader when he has 
perused the work.(^ History is not 
mainly a science which proceeds 
by analysis ; it is the attempt to 

collect and arrange in a living pic- 
ture an enormous mass of detail.^ 
Too rigid definitions, like lines 
which are too hard and marked, 
spoil the total eflfect. 




Thought of 
the present 


ary history, 
to what ex- 
tent possible 
and valu- 

In this sense of the word we have in the following 
treatise to deal with the History of Thought : not, how- 
ever, with the history of thought in general, but with 
that- of a defined period, with that of the present age 
and the age immediately preceding it, — the age, in fact, 
to which the writer and his readers belong, of which 
they have a personal knowledge and recollection more or 
less wide and intimate. It is the latter circumstance 
which has made me select this special portion of the 
history of thought; for it is that portion of which, it 
seems to me, I and my contemporaries should— if we go 
about it in the right way— know most. As every person 
is his own best biographer, so it seems to me every age 
is, in a certain sense, its own best historian. 

We know that this has been frequently denied so far 
as external events (that which many persons call history 
'par excellence) are concerned. Contemporary writers do 
not, it is stated, get beyond mere records of events, 
records at once one-sided, incomplete, and confusing. It 
is indeed necessary to have the records in great number 
and variety : because the true and real record can only 
be given by him who combines all these many records 
into one, who avoids the errors arising from special 
points of view, from narrowness of outlook, from indi- 
vidual ignorance, blindness, or prejudice. Still, in spite 
of such defects, the contemporary records will always 
remain the most valuable sources for the future historian 
who may succeed in sifting their various* testimonies, 
combining and utilising them to produce a fuller and 
more consistent picture of the bygone age. But while 
his work may be only temporarily valuable, theirs is 



lasting. It is hardly doubtful that, after hundreds or 
thousands of years have passed, the simple, detailed, and 
perhaps contradictory, narratives of contemporary wit- 
nesses will outlive those more elaborate and artistic 
efforts of the historian which are so largely inspired and 
coloured by the convictions of another— i;^^., his own- 
age. For as Goethe has remarked : " History must from 
time to time be rewritten, not because many new facts 
have been discovered, but because new aspects come into 
view, because the participant in the progress of an age 
is led to standpoints from which the past can be re- 
garded and judged in a novel manner." i 

Most of the great historians whom our age has pro- 
duced will, centuries hence, probably be more interesting 
as exhibiting special methods of research, special views ' 
on political, social, and literary progress, than as faith- 
ful and reliable chroniclers of events ; and the objectivity 12 
on which some of them pride themselves will be looked fefty 
upon not as freedom from but as unconsciousness on their '^^': 
part of the preconceived notions which have governed 
them. But where the facts recorded and the mind which 
records them both belong to the same age, we have a 
double testimony regarding that age. The events, and 
the contemplating mind, supplement each other to form 
a more complete picture, inasmuch as the matter and the 
medium through which it is viewed belong to the same 
time. And so it comes to pass that historians like 
Thucydides, Tacitus, and Machiavelli are looked upon as 

* Materialien zur Geschichte der 
Farbenlehre,' Werke, 2te Abtheil- 
ung, Band 3, p. 239. I quote from 

the new edition, brought out by 
the German Goethe Society. 





Value of 
ary records, 
both of 
Facts and 


Mystery of 
the Life of 


the material 
for genius. 

perfect models in the art of writing history, and the 
memoirs of many modern statesmen are more lastingly 
valuable than the more elaborate and connected narra- 
tives of remote and secluded scholars. 

But if the contemporary record of facts will always 
have a peculiar value, however incomplete it may be, 
still more must this be the case with the contemporary 
record of thought ; especially if thought means the whole 
of the inner life of an age, not merely that portion which 
in the form of defined thought has been incorporated in 
the written literature of the age. For a large portion of 
this hidden life is known only to those who have taken 
part in it. The vague yearnings of thousands who never 
succeed either in satisfying or expressing them, the hun- 
dreds of failures which never become known, the number- 
less desires which live only in the hearts of men or are 
painted only in their living features, the uncounted 
strivings after solutions of practical problems dictated 
by ambition or by want, the many hours spent by 
labourers of science in unsuccessful attempts to solve 
the riddles of nature, — all these hidden and forgotten 
efforts form indeed the bulk of a nation's thought, of 
which only a small fraction comes to the surface, or shows 
itself in the literature, science, poetry, art, and prac- 
tical achievements of the age. Equally important, though 
not equally prominent, this large body of forgotten, 
thought has nevertheless been that which made the 
measure full, which heaped the fuel ready for the 
match to kindle ; it constitutes the great propelling force 
which, stored up, awaits the time and aid of individual 
talent or genius to set it free. Philosophers tell us of 

the wastefulness of organic life, of the thousands of germs 
which perish, of the huge volume of seed scattered use- 
lessly. A similar fate seems to fall on the larger portion 
of intellectual and moral effort; but here a deeper con- 
viction tells us that it is not the sacrifice but the co- 
operation of the many which makes the few succeed 
that excellence is the prize of united effort, that many 
must run so that one may reach a higher goal. A^at 
other feeling could console those legions of honest workers 
who spend their lives in trying to deal with the seem- 
ingly unconquerable host of social evils, the apparently 
growing vice and misery of large towns, who raise a 
cry for oppressed nationalities, or preach against the 
curses of war and militarism ? Or what higher and un- 
selfish satisfaction could an author derive from spending 
half a lifetime in producing a work which in the end 
may fall dead-born from the press, if it were not the 
conviction that in the cause in which he has failed 
another after him may succeed, and that his failure 
may be a portion of the silent and hidden efforts that 
co-operate towards a useful end ? ^ But who in after- 
ages can write the history of this forgotten and hidden 
work of a nation ? Whose historical sense is delicate 
enough to feel where the pressure was greatest and the 
effort longest ere the new life appeared, whose eye pene- 
trating and discerning enough to follow up the dim streaks 

V 1 *'Sehen wir nun wahrend un- sammen erst der wahre Mensch ist 

seres Lebensganges dasjenige von und dass der EinzeL nur froh 

anderen gelestet wozu wir selbst und glucklich sein kann, wenn er 

fruher einen Beruf fuhlten, ihn aber, den Muth hat, sich im Ganzen zu 

mit manchem andern, aufgeben fuhlen."- Goethe, 'Wahrheft und 

mussten, dann tritt das schone Diehtung,' 9th Book Werke 27 ) 

Gefuhl ein, dass die Menschheit zu- 277. ' vverKe, ^7,y 



ary record 
of Thought 
more faith- 


Events of 
the imme- 
diate past. 

of twilight, dazzled as he must be by the blaze of the 
risen sun ? We who live in the expectation of the light 
which is to come, surrounded by the shadows, difficulties, 
and obstacles ; we who belong to the army, and are not 
leaders, who live in, not after, the fight, — we claim to be 
better able to tell the tale of endless hopes and endeav- 
ours, of efforts, common to many, of the hidden intellec- 
tual and moral work of our age.^ 

How far back we who have lived during the second 
half of the present century may extend the period of 
which we claim to have a personal knowledge, is a point 
of further interest. Certain it is that in our parents and 
immediate forefathers we have known the representatives 
of a generation which witnessed and laboured in the in- 
terests of the great Anti-Slavery, the Keform, and the Anti- 
Corn-Law movements, who experienced the revolutions 
worked by the introduction of steam-power and gas, who 
took part in the great work of national and popular edu- 
cation abroad and in the reform of school-life in England. 
They themselves went through the enthusiasm of the 
anti-Napoleonic Kevolution in Germany, came under the 
influence of Goethe's mature manhood, were fascinated by 
the stories from the pen of the Wizard of the North, par- 

^ Compare what A. de Tocqueville 
says, ' (Euv. comp.,' vol. viii. p. 170 : 
* ' Nous sommes encore trop pres des 
ev^nements pour en connaitre les 
details. Cela parait singulier, mais 
est vrai. Les details ne s'appren- 
nent que par les revelations post- 
humes, conteiiues dans les M^- 
moires, et sont souvent ignores des 
contemporains. Ce qu'ils savent 
mieux que la posterite, c'est le 

mouvement des esprits, les pas- 
sions generales du temps, dont ils 
sentent encore les derniers fr^mis- 
sements dans leur esprit ou dans 
leur cceur ; c'est le rapport vrai des 
principaux personnages et des prin- 
cipaux faits elitre eux. Voilb, ce 
que les voisins des temps racont^s 
apergoivent mieux que ne fait la 



took of the spirit of the Eomantic School, felt the electrical 
touch of Lord Byron s verse, listened to the great orators 
of the third French Eevolution, and could tell us of the 
now forgotten spell which Napoleon I. exercised over 
miUions of reluctant admirers. Most of these fascinations 
and mterests live only in the narratives of contemporaries 
and surviving witnesses, few of whom have succeeded in 
perpetuating them with pen or brush, making them intel- 
ligible to a future age ; most of them die with the genera- 
tion Itself. Not only have we listened to their words and 
seen in their features the traces of the anxieties they lived 
through, in their eyea the reflected enthusiasms and as- 
pirations, in their glances and in the trembling of their 
voices the last quiverings of bygone passion and joy —we 
- have received from them a still more.eloquent testimonial 
a more hving inheritance. But this we cannot hand 
down to our children in the form in which it was given 
to us : it has not passed through our hands unaltered 
This inheritance is the language which our parents have- 
taught us. Unknowingly they have themselves altered 
the tongue, the words and sentences, which they received 
depositing in these altered words and modes of speech the' 
spirit, the ideas, the thought of their lifetime. These 
words and modes of speech they handed to us in our 
infancy, as the mould wherein to shape our minds, as the 
shell wherein to envelop our slowly growing thoughts, as 
the instrument with which to convey our ideas. In their 
language, in the phrases and catchwords peculiar to them 
we learnt to distinguish what was important and interest- 
ing from what was trivial or indifferent, the subjects which 

which Lan- 
guage under- 
goes from 
parent to 
child, a 
proof of the 
life of 

of conven- 
speech for 
Coining of 
new words. 


Should occupy our thoughts, the aims we should follow 
the principles and methods which we should make use ot. 
The bulk and substance of this they indeed inherited them- 
selves ; but the finer distinctions of their reasonmg, the 
delicate shading of their feelings and aspirations, they 
added and modified for themselves, modelling for their own 
special use the pliable and elastic medium of the mother 
tongue. With this finer moulding we have inherited the 
spirit of the former generation : predisposing us to certam 
phases of thought and placing in our path a difficulty m 
acquiring otherwise than by gradual and almost imper- 
ceptible degrees the faculty of assimilating new and mi- 
expected opinions, tastes, and feelings. Many of us adhere 
to the special character and phase of thought acqmred 
in our youth. Some by learning foreign languages, and 
living in other countries, gain a facility for understandmg 
quite difierent phases of thought: very few among us 
develop so much original thought that they burst the 
shell of conventional speech, coining new words and ex- 
pressions for themselves, embodying in them the fleetmg 
ideas of their time, the indefinable spirit of their age. 
Once expressed, these new terms are rapidly circulated, 
and if we look back on the period of a generation, we 
note easily the progress and development of opinion and 
tastes in the altered terms and style of our language. 

Thus it is that the writer, and those of his readers 
whose memory carries them back to the middle of the 
century, and whose schooling and education embodied the 
idea^ of a generation before that time, can claim to have 
some personal knowledge of the greater portion of the 
nineteenth century, of the interests which it created and 



the thoughts which stirred it.^ It is the object of these 
volumes to fix, if possible, this possession ; to rescue from 
oblivion that which appears to me to be our secret prop- 
erty ; in the last and dying hour of a remarkable age to 
throw the light upon the fading outlines of its mental 
life ; to try to trace them, and with the aid of all possible 
information, gained from the written testimonies or the 
records of others, to work them into a coherent picture, 
which may give those who follow some idea of the 
peculiar manner in which our age looked upon the world 
and life, how it intellectualised and spiritualised them. 
This attempt is therefore not a history of outward politi- 
cal changes or of industrial achievements : the former will 
probably be better known to our children than they have 
been to us ; the latter will soon be forgotten as such, or 
incorporated in the still greater results of the future, for 
which they will be the preparation. Nor is it a history 
of Knowledge and Science, of Literature and Art, which 
I purpose to write ; though as these are the outcome of 
the inner life, and contain it, so to say, in a crystallised 
form, they will always have to be appealed to for the 
purpose of verifying the conclusions which we may arrive 

Object of 
this work 
to retrace 
the life of 
through the 
dying cen- 

Not a politi- 
cal history, 
nor a history 
of Science, 
and Art. 

^ On the division of History into 
centuries see what Du Bois-Rey- 
mond says ('Reden,' Leipzig, 1886, 
vol. i. p. 519), and the fuller dis- 
cussion of the subject by Prof. O. 
Lorenz, * Die Geschiehts - wissen- 
schaft' (Berlin, 1886, p. 279 9qq.) 
The latter refers to what the first 
historian says (Herodotus, ii. 142 : 
Katroi rpirtKOffiai fxkv avSpuv yfveal 
ivvtarcu fiijpia. ^rea • yfvfal ykp rpus 
au^puv (Karbv freet ian). A per- 
son born in 1840 can claim to have 
a personal knowledge of the last 

half, and through his parents and 
teachers a knowledge of the first 
half, of the century. In this way 
it may be said that his personal — 
direct or indirect — knowledge ex- 
tends over nearly a century. Lor- 
enz says correctly : " Fiir jeden 
einzelnen bildet der Vater und der 
Sohn eine greifbare Kette von 
Lebensereignissen und Erfahrun- 
gen." And that this applies even 
more to ideas and opinions^ to 
Thought, than to events and facts, 
is evident. 





Where the 
interest of 
the book 
will lie : 
in all the 
•which have 
a result on 
our inner 

The personal 
and experi- 
ence neces- 
sary for a 
true por- 
trayal forms 
a limitation 
of the ex- 
tent of 
ground to be 


at. What will interest us most will be the conscious 
aims and ends, if such existed, of any political or social 
movement, and, where they did not exist, at least the 
results to our inner life which have necessarily followed, 
the methods by which knowledge was extended or science 
applied, the principles which underlay literary composition 
and criticism, and the hidden spiritual treasure which 
poetry, art, and religious movements aimed at revealing 
or communicating ; in fact the question : What part has 
the inner world of Thought played in the history of our 
century, — what development, what progress, what gain 
has been the result of the external events and changes ? 
But if personal knowledge and experience are— as it 
seems to me — of the greatest importance in an attempt 
like this ; if, without having lived the inner life, a record 
of it would be either a mere string of names or a criticism 
of opinions, not a living picture, — so it is also the factor 
which necessarily limits the extent of the ground which 
I propose to traverse. Thus I feel obliged in the first 
place to limit myself to European Thought. Such a limi- 
tation would hardly have been called for a century ago, 
because it would have been a matter of course : but the 
steady growth and peculiar civilisation of a new and 
vigorous people on the other side of the Atlantic force 
from me the twofold confession, that there is a large 
world of growing importance of which I have no personal 
knowledge, and to estimate which I therefore feel un- 
qualified and imprepared ; and further, that I am equally 
unable to picture to myself the aspect which the whole of 
our European culture in its present state may assume to 
an outside and far-removed observer who is placed in the 

New World. As this New World grows not only in 
numbers and national wealth, but also in mental depth, 
as it becomes more and more intellectualised and 
spiritualised, so it will no doubt experience the desire of 
recording its own inner life and culture, emphasising the 
peculiarities which distinguish it as a whole from our 
civilisation. But the tendencies of this new culture are 
to me vague and enigmatical, and I frankly admit that 
I am unable to say anything definite on this subject. Con- 
vinced as I am that in human affairs all outer life is the 
vessel which contains an inner substance, the shell which 
envelops a growing kernel, I am, nevertheless, unable in 
this case to penetrate to either, and must therefore content 
myself with taking notice of this vast new element of 
nineteenth-century culture only where it comes into 
immediate contact with European thought, which has 
indeed been powerfully influenced by it. And of Euro- 25 
pean thought itself I am forced to select likewise only GelX^""' 
the central portion, the thought embodied in French, ^f^e 
German, and English Literature. I have to admit that Sr'"''^ 
Italian, Scandinavian, and Eussian influences are all ''°' ' 
around this centre, sometimes penetrating far into it; 
but here again languages unknown and interests foreign 
to me have made it impossible to identify myself ever so 
superficially with the new life that is contained in them. 
I must therefore here also confine myself to very im- 
perfect and casual notices, which make no attempt to 
do justice to the subject. 

The subject before us, then, is European Thought— i.e., 
the thought of France, Germany, and England— during the' 
greater part of the nineteenth century. Circumscribed as 




Unity of 
Thought a 
of this 




this subject is by the limits of time and space which I 
have mentioned, it is, nevertheless, still vast, intricate, and 
bewildering. And yet it is my intention, throughout the 
inquiries which I have to institute and in the various out- 
lines and sketches which I have to draw, never to lose 
sight of the unity of the whole. This unity, I maintain, 
the progress of our age has more and more forced upon 
us. It is itself a result of the work of the century. A 
hundred years — even fifty years — ago, it would have been 
impossible to speak of European Thought in the manner 
in which I do now. For the seventeenth and eighteenth 
centuries mark the period in which, owing to the use of 
the several vernacular languages of Europe in the place 
of the mediseval Latin, thought became nationalised, in 
which there grew up first the separate literature and then 
the separate thought of the different civilised countries of 
Western Europe. Thus it was that in the last century, 
and at the beginning of this, people could make journeys 
of exploration in the region of thought from one country 
to another, bringing home with them new and fresh ideas. 
Such journeys of discovery, followed by importation of new 
ideas, were those of Voltaire^ to England in 1726, where 
he found the philosophy of Newton and Locke, at that 
time not known and therefore not popularly appreciated 
in France; the journey of Adam Smith in 1765 to France, 
where he became acquainted with the economic system of 
Quesnay and the opinions of the so-called " physiocrats," 
which formed the starting-point of his own great work. 

^ For a most complete collection 
of data referring to this subject 
see Du Boia-Reymond's address in 

the Berlin Academy, -SOth January 
1868, reprinted in the collection of 
his * RedcE ' Leipzig, 1886, vol. L 



* The Wealth of Nations.' During the last quarter of the 
eighteenth century A. G. Werner raised the Mining 
Academy at Freiberg, which had been founded in 1766, 
from a mere provincial institution to be one of the great 
centres of scientific light in Europe, to which students 
from all parts of the world flocked to listen to his eloquent 
teaching. Towards the end of the century Wordsworth 
and Coleridge went on a trip to Germany, whence the 
latter brought to England the new philosophy of Kant 
and Schelling. Madame de Stael, in an age when tidings 
of a new literary life in Germany had reached French 
Society through some of the emigrants of the Eevolution, 
set herself reluctantly to learn German,^ convinced that a 
n^w phase of thought had appeared there ; and then with 
Benjamin Constant visited the country itself at the end 
of 1 8 3, and again in 1 8 7. The result of these journeys 
of exploration was her work ' De L'Allemagne.' Whilst 
Coleridge and Madame de Stael drew inspiration from 
the new life which centred in the Weimar of Goethe and 
Schiller, the scientific students of the whole Continent 
directed their gaze to Paris, where alone for many de- 
cades the modern methods could be learnt, where the 
new scientific ideas were, so to speak, collected in a focus. 
For more than half a century Paris remained the centre 
of scientific thought,^ and even English philosophers, who 

brought to 
England by 
and Words- 


into France 
by Madame 
de Stael. 

Paris the 
focus of 

^ See Lady Blennerhasset's in- 
teresting work on Madame de Stael, 
German ed., vol. ii. p. 461 sqq, ; 
especially the remarkable passage 
quoted there, p. 465, in her letter 
to the Baron de Gerando, October 
1802: "Ich glaube wie Sie, dass 
der menschliche Geist, der zu wan- 

VOL. I. 

dern scheint, jetzt bei Deutschland 
angelangt ist." 

2 See Bruhns, 'Life of A. v. Hum- 
boldt,* translated by Lassell, vol. i. 
p. 232 : " Notwithstanding the 
sardonic expression of the frantic 
judge, ' Nous n'avons pas besoin de 
savans,' Paris was yet at the close 




cal methods 
into Eng- 
land by 
and Pea- 




shown to his 
own country 
by an Eng- 

since Bacon and Newton had foUowed their own inde- 
pendent line of research, had to discover in the second 
decade of the century that Newton's great name was not 
a guarantee for the efficiency of his methods, which had 
been greatly developed and improved in the hands of 
Continental mathematicians. These improved methods 
were imported into England by three Cambridge grad- 
uates, Herschel, Babbage, and Peacock, who translated 
Lacroix's Treatise, and by doing so gave a great impetus 
to mathematical research in this country. Fifteen years 
later, students from all parts of the world flocked to the 
small University town of Giessen in Germany, thence to 
take home with them a knowledge of the new science and 
methods of Chemistry, taught in the laboratory of Liebig— 
methods previously used only in the private and inacces- 
sible laboratories of learned investigators.^ It will be in 
the memory of many how the philosophy of Auguste 
Comte, published between the years 1830 and 1840, 
remained without much influence in his own country, 
whereas, mainly through the writings of J. S. Mill and 

are good, and successfully accom- 
plish their main object in the 
diffusion of mathematical know- 
ledge.'" Compare also vol. i. p. 
342, referring to 1804. Also vol. ii. 
p. 92, referring to the period 1820 
to 1830. "Humboldt continued 
to regard Paris as the true metro- 
polis of Science " (p. 70), and many- 
other passages. See also Steffens, 
" Was ich erlebte," vol. x. p. 233, 
and what Goethe said to Eckermann 
on the contrast of Germany and 
Paris in the year 1827. 
' 1 See A. W. Hoffmann, *The 
Life -Work of Liebig,' Faraday 
Lecture for 1875, p. 8. 

of the eighteenth century the 
metropolis of the exact sciences. 
Lalande, in writing to von Zach on 
January 26, 1798, remarks: 'The 
love of mathematics is daily on 
the increase, not only with us but 
in the army. The result of this 
was unmistakably apparent in our 
last campaigns. Bonaparte himself 
has a mathematical head, and though 
all who study this science may not 
become geometricians like Laplace 
and Lagrange, or heroes like Bona- 
parte, there is yet left an influence 
upon the mind which enables them 
to accomplish more than they could 
possibly have achieved without this 
training. Our mathematical schools 

: > 




his school, it became, as it were, a centre of thought, an 
embodiment of a circle of modern ideas in this country, 
whence it was reimported into France nearly a generation 
after its first appearance. Something similar happened 
to a once neglected but now renowned English landscape- 
painter, Constable, whose pictures when exhibited in 35. ■ 
France in 1824 created a profound sensation, and had ?X^^lt 
such an influence on the artists of that country that they ^''''' 
are said to mark an era in landscape-painting there.^ 

Such journeys of discovery in the realm of thought and 
ideas have now become almost impossible. In the course 
of our century Science at least has become international : 36. 
isolated and secluded centres of thought have become comeln^";- 

1 nntinnal 

more and more rare. Intercourse, periodicals, and learned 
societies with their meetings and reports, proclaim to the 
whole world the minutest discoveries and the most recent 
developments. National peculiarities still exist, but are 
mainly to be sought in those remoter and more hidden 
recesses of thought, where the finer shades, the untrans- 
latable idioms, of language suggest, rather than clearly 
express, a struggling but undefined idea. Thought has its 
dawn and twilight, its chiaroscuro as well as its open day ; 
but the daylight has grown wider and clearer and more dif- 


^ See Walter Armstrong in the 
'Nineteenth Century' for April 
1887; Julius Meyer, 'Geschichte 
der modernen franzosischen Mal- 
erei,' Leipzig, 1867, Book 7, chap. 
2 ; A. Rosenberg, * Geschichte der 
modernen Kunst,' vol. i. p. 63. 
Rosenberg thinks the influence of 
Constable on French Art is exagger- 
ated, and mentions Paul Huet, 
whose early pictures date from 
1822. But an Englishman, Bon- 
ingtoD, who, however, is claimed as 

of the French School, was even 
before Huet and Constable. See 
also what Delacroix wrote to Th. 
Sylvestre in 1858 : " Constable est 
une des gloires anglaises. C'est un 
veritable r^formateur, sorti de I'or- 
niere des paysagistes anciens. Notre 
^cole a grandement proflt^ de ses 
examples et G^ricault ^tait revenu 
tout etourdi de I'un des grands pay- 
sages qu'il nous avait envoyds" 
(quoted by Emile Michel in * Grande 
Encyclopedic, ' art. " Constable " ). 






The light 
which Ety' 
throws on 
history of 

and on the 
of ideas. 

fused in the course of our century, and so far as the greater 
volume of ideas is concerned, we can speak now of Euro- 
pean thought, when at one time we should have had to 
distinguish between French, German, and English thought. 
Eeserving, therefore, in the meantime the task of investi- 
gating what still, within the bounds of this larger inter- 
national life, remains peculiar to the thought of each 
nation, it is the great body of common European thought 
with which I propose at first to deal. How has it grown 
to be what it is now, what special contributions have the 
several nations made to the general stock, what is at 
present our inventory of it, how has it been changed in 
course of the century ? But how, it may be asked, are we 
to take stock ? how is this inventory to be drawn up ? 
There is indeed one very obvious method which presents 
itself, though it is not the one which I propose to use 
exclusively, or even largely. And yet it seems to me 
well worthy of special attention. 

Already I have remarked how the changes of thought 
are deposited in the altered language and style of the 
age. A closer study of the changes which, in the course of 
this century, have taken place in the vocabularies as weU 
as in the styles of the three principal European languages 
would no doubt reveal to a great extent when and how 
new ideas have presented themselves, how they have 
become fixed and defined in special words or terms. It 
would allow us to trace to a very large extent not only 
the growth of the general stock of European thought, but 
also the migration of single ideas from one nation to 
another. And, lastly, it would exhibit to a great extent 
in what peculiar phrases, in what secluded corners, the 

individual thought of each of the three nations has found 
refuge.^ Any one who has attempted to translate from 
one of these languages into another, be it prose or be 
it lyrical, philosophical, or descriptive poetry, will have 
experienced the necessity of studying minutely the 
meaning or hidden thought which a word or a phrase 
may signify: he will have been led to notice what is 
common and what is peculiar to different languages, 

^ The only books which treat 
of words in the sense mentioned 
above, and which have come under 
my notice, are Home Tooke's * Di- 
versions of Purley ' and Archbishop 
Trench's little volumes on 'The 
Study of Words' and 'English 
Past and Present.' So far as the 
use of merely philosophical terms 
is concerned, I may refer to R. 
Eucken, 'Geschichte der philoso- 
phischen Terminologie,' Leipzig, 
1879. A great deal of material 
for a research of this kind may 
be found in the large Dictionaries 
of Grimm, Littre, and Murray, 
though I do not feel sure that the 
great change which has come over 
language, through the expansion, 
deepening, and differentiation of 
ideas and of thought in our age, 
has been specially taken note of. 
The plan of Orimm's Dictionary, 
which aims at embracing the Ger- 
man language in its development 
during three centuries, beginning 
with Luther and ending with 
Goethe (see Wilh. Grimm's 'Kleinere 
Schriften,' vol. i. p. 508), almost 
excludes the period which I am 

It is interesting to remember 
that Diderot, the first writer who 
attempted to collect the great body 
of modern Thought and Learning 
into an encyclopaedic whole, re- 
ferred to Language very much in 
the same manner as we do now, 
a hundred a«d ififity jears later. 

See the article " Encyclopddie, " 
where Diderot says that a Dic- 
tionary is only an exact collection 
of titles, to be filled in by the Ency- 
clopaedia ; and further on, p. 639 : 
"Si Ton compte les hommes de 
g^nie, et qu'on les repande sur 
toute la duree des siecles ecoules, 
il est Evident qu'ils seront en petit 
nombre dans chaque nation et pour 
chaque siecle, et qu'on n'en trouvera 
presqu'aucun qui n'ait perfectionnd 
la langue. Les hommes createurs 
portent ce caract^re particulier. 
Comme ce n'est pas seulement en 
feuilletant les productions de leur 
contemporains qu'ils rencontrent 
les idees qu'ils ont k employer dans 
leurs ecrits, mais que c'est tantot en 
descendant profond^ment en eux- 
memes, tantot en s'elan^ant au 
dehors, etportantdes regards plus 
attentifs et plus p^n^trans sur les 
natures qu'ils environnent, ils sont 
obliges, surtout a I'origine des 
langues, d'inventer des signes pour 
rendre avec exactitude et avec force 
ce qu'Cs y decouvrent les premiers. 
C'est la chaleur de I'imagination et 
la meditation profonde qui enrichie- 
sent une langue d'expressions nou- 
velles : c'est la justesse de 1 'esprit 
et la sev^rite de la dialectique qui 
en perfectionnent la syntaxe ; c'est 
la commodity des organes de la 
parole qui I'adoucit; c'est la sen- 
sibility de I'oreille qui la rend har- 





of the 


Growth in 
the mean- 
ings of 

and the thought which they express. Of Goethe it 
may be said that he created to a large extent the 
language and style of that which is best in the modern 
literature of his country. No such supreme influence 
belonging to a single individual can probably be found 
in any other German, French, or English writer in our 
century, for reasons which are obvious : but the great 
French novelists, the German metaphysicians, and the 
original poetical minds of modern England have en- 
larged and enriched the vocabulary of their respec- 
tive languages, and have added a number of useful 
and novel modes of expression (tournures, Wendungen). 
Carlyle's influence has been great in inti'oducing novel 
epithets, borrowed or imported frequently from the 
German. Matthew Arnold has laboured in a similar 
direction, his models being, besides Goethe and Heine, 
mostly French authors, such as Sainte-Beuve and the 
introspective school. Germany has been less fortunate 
in extending her vernacular vocabulary : the facility 
which her language possesses of assimilating foreign words 
and using them almost without any alteration has done 
much to complicate German style, destroying its sim- 
plicity, its graces, the poetical element. It will, however, 
probably be found that by far the greatest accession to 
the vocabularies — though not to the finer modelling — of 
the modern languages has come from the influence of the 
sciences on general culture and literature. Well-known 
words, long in use, have at the same time through this 
influence acquired altered or more specific meanings. 

The vaguer word " development " has been supplanted 
by "evolution." "Differentiation" has a definite philo- 



Sophie — not only a mathematical — meaning. The word 
" positive " has, besides the logical signification, acquired 
at least two meanings which are very specific, and 
which it did not possess formerly. "Energy" has, 
besides the general meaning, and the philosophical one 
which Aristotle assigned to it, acquired a special meaning, 
having first in England and then abroad taken the place 
of "force" as a more correct and definable term. In 
connection with it, " correlation " and " conservation " are 
terms of very specific value. The word "fittest" and the 
phrase " struggle for existence " mean something different 
from what they meant fifty years ago. Then there are 
the terms "exact" and "science" themselves, which mean 
something different now from what they meant formerly. 
And coming out of the more recent doctrines of the limits 
of human and conscious individual knowledge, there are 
the words " unconscious," " unknowable," and " agnostic," 
which indicate whole trains of novel thought. It would 
indeed be an interesting and useful investigation to follow 
up to their origin the many new words and phrases, or 
the altered meanings of well-known and familiar words, 
in which the three principal European languages abound. 
It would be a methodical study of the changes which 
thought has undergone. 

Nor need such an undertaking be based upon any 
particular or one-sided theory as to the connection of 
Civilisation, Thought, and Language. This century has 
not been wanting in such, from the extreme theory of 
De Bonald,^ who saw in Language an immediate Divine 
revelation, to the most recent and more scientific view 

^ DeBonald (1754-1840), 'L^islation primitive,' Paris, 1802. 


has found 
new words. 

De Bonald's 
theory of 
and Max 
Science of 





of Max Miiller, who would absorb philosophy in the 
science of Language^ in the same way as Astronomy has 
to many become merely " une question d'analyse." In a 
certain sense we can agree with both of these thinkers. 
Without discussing the vexed question of the origin of 
Language and Thought, to us as individuals, born in a 
civilised and intellectual age, words certainly came earlier 
than clear and conscious thought. The easy manner also in 
which, through the use of our parents' tongue, we became 
introduced into a complex and bewildering labyrinth of 
highly abstract reasoning is little short of a miraculous 
revelation. But, as I mentioned above, it is not my 
intention to study the development of European thought 
during this century by means of a close analysis of the 
changes and growth of the three principal languages. 
Such an enterprise would demand an amount of lexico- 
graphical knowledge possessed only by the authors of 
dictionaries like those of Grimm, Littre, and Murray. 
But though I am not qualified for such a task, there is one 
special point on which I cannot avoid being drawn into 
a grammatical discussion. It refers to the word Thought 
itself. How is the meaning which I and my readers con- 
nect with this word to be expressed in French and Ger- 

pressea in 

French^and j^qj^ ? How are wc to translate the word ? The subject we 
deal with does not belong to England alone, but as much 
to France and to Germany : it must thus have a name in 
each of their languages. Now I believe that the word 
pens^e expresses in French very nearly the same thing 
which we mean in English by thought. It is some- 

^ See his ' Science of Thought, ' London, 1 887, especially pp. 292 and 


how ex- 
iressed in 
French a: 

what more difficult to find a corresponding word in Ger- 
man. I have for some time hesitated whether to use the 
word Geist or Weltanschauung, two terms frequently used 
to express the aggregate of the inner life of an age : but 
have finally resolved to use the word Denken, as this word 
lends itself to the same contrasts of Life and Action 
{Leben und Handeln), denoting the inner world, whereas 
the opposite of Geist is /S/Jo/ (matter), and Weltanschauung, 
though an expressive and untranslatable word, denotes 
rather the outcome, the result, of thought than thought 
itself. Passing from the word to the subject itself, I find 
that the greater definiteness of the term in the English 
language is accompanied also by a more abundant litera- 
ture of the subject. The larger idea of a Philosophy of 
History is indeed due mainly to Continental thinkers, o'msX^ 
especially to Herder, Hegel, Comte, and Guizot, and t^^^?"' 
Voltaire's ' Si^cle de Louis XIV.' will always be the ^^''^'''' 

model of the historical picture of a period. Still it is 

in my opinion— mainly the writings of Carlyle, Buckle, 
Draper, Lecky, Leslie Stephen, and, considering its size, 
perhaps more than all, Mark Pattison's * Essay,' ^ which 
have fixed in our minds the meaning of the word 
Thought as the most suitable and comprehensive term 
to denote the whole of the inner or hidden Life and' 
Activity of a period or a nation. I therefore put in a 
claim to start with the use of the English word, as 
sufficiently familiar \o most of my readers, and request 
those who may object to the vagueness of the French 


^ See * Essays and Reviews,' 
* Tendencies of Religious Thought 
in England, 1688-1750,' by Mark 
Pattison; also Leslie Stephen's 

remarks on it in the Preface to \ 
his * History of English Thought / 
in the Eighteenth Century.' 



Want of 
precise term 
in German 
and French. 

of Thought 
less not spe- 

Carlyle the 
first to give 
a special 
meaning to 
the word 

and German equivalents tc look for a definition of my 
intention in the English word "Thought." I am not 
aware that French literature possesses any " histoire de 
la pens^e," either of a longer or shorter period ; I know 
of innumerable works in German which cover a similar 
field, but they have mostly used the word Weltanschauung, 
or expanded the meaning of Thought into the wider sense 
of a history of Civilisation (Kulturgeschichte) or narrowed 
it to that of Literature, proving — as it seems to me — 
the real want of a concise term such as the English 
language now supplies. And yet, I think I am right 
in saying that the conception of Thought, in the sense 
in which I am using it, is truly an outcome of interna- 
tional, not of specifically English progress, and belongs 
mainly to the period of which I am treating, — a period 
characterised, as I have already remarked, by the great 
interchange of ideas, by the breaking down of intellectual 
barriers, between the principal European nationalities. 
It was above all in the mind of Thomas Carlyle, who first 
among Englishmen made a profound study of the intel- 
lectual agencies which brought about the great change in 
modern Europe, that the conception formed itself of an 
intellectual and spiritual organism, underlying and moving 
external events. He first gave the peculiar sense to the 
word Thought, in which we here employ it, and made it 
an object of special study for those who came after him ; 
an object, indeed, definable in various ways and to be con« 
templated from differing points of view, but yet a some- 
thing, a power recognised by every one, and for which no 
better word could be invented. No other language has a 
word so comprehensive, denoting at once the process and 



the result, the parts and the ideal whole, of what is felt 
and meant : it commits us to no preconceived theory, 
can be used equally by thinkers of the most opposite 
views, and lends itself to any specialisation which may 
become necessary. 


Two processes have helped to determine the intel- 
lectual progress of mankind. These two processes have Sitoi^of 

/?, •, ^ intellectual 

otten been apparently opposed to each other in their P^g^ess. 
operations ; but in reality neither of them can proceed 
very far without calling the other into existence. They 
are the extension and the condensation of knowledge. 
Curiosity, the demands of practical life, the experiences 
of every day, all tend to an enlargement, to an accumula- 
tion of knowledge. Such growing knowledge is, however, 
of little avail if it be not readily grasped : the command 
of knowledge is as important as its accumulation. The 
more extensive the country which we wish to explore, the 
more we look out for elevated and commanding points 
of view, which permit us at a glance to overlook a wide 
landscape measuring the distance behind or the prospect 
before us. But, however enticing, these elevated views 
are frequently seductive and misleading. They permit us 
not only to look backward on the land which we have 
explored, giving us a clearer picture of its many features, 
of its winding paths, of the position of its separate objects 
— these elevated views present to us likewise the regions 
which we have not yet explored, and suggest the attempt 
to supersede the laborious process of further exploration 


Object of 
the book. 




century un- 
equalled in 
tion of 

by the more delightful venture of fillmg up the dim out- 
lines which we see before us, with analogies of past ex- 
perience or creations of our imagination. And even if 
we do descend into the plains and continue the minuter 
and more laborious search, we cannot rid ourselves of cer- 
tain preconceived but frequently misleading ideas which 
the superficial glance has impressed on our minds. 

The condensation may become an idealisation of know- 
ledge. History affords numerous examples of these dif- 
ferent stages of progress ; centuries of dull accumulation, 
of unmethodical and ill-arranged learning, have been fol- 
lowed by short periods of enlightenment, by the trium- 
phant shout of sudden discovery or the confident hope of 
invention. Patient work and real progress have for a long 
time been repressed by the allurements of seductive phan- 
toms, which have had to be abandoned after an immense 
waste of labour. New prospects have suddenly opened 
the view into vast unexplored regions, heights have been 
gained from which the whole of human knowledge ap- 
peared for the moment condensed into a single truth or 
idealised into a vision, and again these delightful achieve- 
ments have for a time appeared lost in an all-pervading 
discouragement and dismay. 

Whether our century has been characterised by any 
one or by a succession of several of these varying moods, 
is a question which I hope to answer in the sequel. For 
the present it is sufficient to note that in both directions — 
in that of accumulating and in that of condensing and 
idealising knowledge— the efforts of the nineteenth cen- 
tury have been many and conspicuous. In the former it 
is altogether unparalleled, whereas in the latter it has 



probably not equalled the ideal greatness of Greece in 
the Periclean age, the brilliancy of the Eenaissance in 
Italy, or the great discoveries of the sixteenth and seven- 
teenth centuries in France and England. But what our 
century has done is this : it has worked out and deposited 
in special terms of language a clearer view of the correct 
methods for extending knowledge, and a peculiar concep- 
tion of its possible unity. At one time — and that not 
very long ago — the word truth seemed to indicate to the 
seeker not only the right method and road for attaining 
knowledge, but also the end, the crown of knowledge. 
" Truth, and nothing but truth," seems still to the popular 
mind the right maxim for seeking knowledge — the whole 
truth stands before it as the unity of all knowledge, were 
it found. I think it is now sufficiently clear to the scien- 
tific inquirer, as well as to the philosopher, that love of 
truth, while it does indeed denote the moral attitude of the 
inquiring mind, is insufficient to define either the path or 
the end of knowledge. " What is truth ? " is still the un- 
solved question. The criteria of truth are still unsettled. 
It would, indeed, be a sorrowful experience, a calamity of 
unparalleled magnitude, if ever the moral ideas of truth 
and faith should disappear out of the soul of either the 
active worker or the inquiring thinker ; but it is with 
these as with other treasures of our moral nature, such as 
goodness and holiness, beauty and poetry — our knowledge 
of them does not begin, nor does it increase, by definition ; 
and though in the unthinking years of our childhood we 
acquire and appropriate these moral possessions through 
the words of our mother-tongue, they rarely gain in depth 
or meaning by logical distinctions which we may learn, 

what it has 
achieved : 
a. Method 
of know- 
ledge ; 6. un- 
ity of know- 

Search after 
truth not 
the end of 
only the at- 
titude of 
the inquir- 
ing mind. 



Method of 
first by 
Newton, &c 
defined by 
Mill, &c. 

tion of 
only ap- 

or to which we have to submit, in later life. These do 
not touch the essence, though very frequently they may 
succeed in destroying the depth, of our convictions. 

In the place, then, of the high-sounding but indefinable 
search after truth, modern science has put an elaborate 
method of inquiry: this method has to be learnt by patient 
practice, and not by listening to a description of it. It is 
laid down in the works of those modern heroes of science, 

., from Galileo and Newton onward, who have practised it 
successfully, and from whose writings philosophers from 
Bacon to Comte and Mill have — not without misunder- 
standing and error — tried to extract the rationale. These 
methods will take up a large portion of our attention. 

(For the moment it is important to note that the result or 
aim of scientific inquiry does not dictate the methods, — the 
purely scientific inquirer does not know where the path 
will lead him : it is sufficient that it be clearly marked. 
Modern science defines the method, not the aim, of its 
work.J It is based upon numbering and calculating — in 
short, upon mathematical processes ; and the progress of 
science depends as much upon introducing mathematical 
notions into subjects which are apparently not mathe- 
matical, as upon the extension of mathematical methods 
and conceptions themselves. The terms "exact" and "posi- 
tive" are current in the Continental and English languages 
to denote these methods and their application. Now to 
any one who does not stand in the midst of the scientific 
work of the age, it might appear as if by merely following 
a defined method which is capable of numerous modifica- 
tions, — by treading a clear path which in its course leads 
us to endless equally defined ramifications, — the scientific 



"er h \ ''? ""^ ^"^^ --« tJ^- elevated 

V w. those points of condensation, those unifying and 
Kleahsing aspects on which, as it seems to us the com 

a most .nevz^w so far as the older ideas are con- 
cerned Unity of knowledge, order and harmony, even 

nXTl:""' ^'""^'^^' *™^^ ^^'^ '^^^'y' -indeed ' 

no longer of direct use as canons for the scientific inquirer 

:Tt" ? ™'^*"^" ^'^'^^ ^"PP°-^ *° »>« -hereS 

m certain numbers. Though we still live under the 

charm of such entities, however much we may try to get rid 

of them, It must nevertheless be admitted that the poetical 

philosophical, and religious aspects of things seem to" cede s 

guide scientific search : it does not receive from them much -- .a 
support. Have both sides been losers by this change. ^°'"^- 
So ar as science is concerned, it can claim to have attained 
by It not only a greater formal completeness and certainty 
o^progress, but also another very important advantage 
^vhlch was unknown to ancient and medi.^val research. 

This advantage consists in the closer connection be- , 
piritThZ "' '"'""' "'" ^'^ " mathematical S™ 
commeree, and industry, and is gradually penetrating into "'• 

For T:r'' "'' " "^'"'"^' ^^"' ^"'^ administration 
For all these pursuits have either directly to do with 

numbers, measures, and weights, with distances of space 
and time, or thev havp fn^n^ ;f ^ 

.n .1 u \ '^ necessary to introduce 

an elaborate system of ^tati^i^ina o«^ 

-^ statistics and averages through 

and individual influences are practically eliminated. The 



problems of scientific research have thus enormously in- 
creased ; each advance in science increases our command 
of certain measurable phenomena in practical life ; each 
^ew development in the latter prepares a new field for 
scientific inquiry. The contact between science and life 
has become more intimate in the course of our century. 
This to a great extent has counterbalanced the tendency 
of modem scientific method, which, operating alone, would 
have led to endless specialisation ; for it is the peculiarity 
,0 of all practical problems that they cannot be isolated m 
TX^ci' the same way bb scientific experiments-that they, in fact, 
'"''^""- force upon us the necessity of looking at a large number 
of surrounding and extraneous circumstances, at the total- 
ity of life and its interests.^ 

If our century can claim to have firmly established 
exact or positive methods in science and life, and to have 
furthered in this way the interests of both, the question 
„ remains, Has nothing been done to uphold those older, 
S^tr those time-haUowed ideals of truth, beauty, and wisdom 
dcSr ^hich to former ages seemed to denote the unifying and 
^"^^ harmonising principles of science and life ? What has 
become of philosophy, art, and religion, which were once 
intrusted with the special care of those ideals, charged 
with preventing the falUng asunder of the many branches 
of knowledge and practice, and expected to save us from 
a loss of the belief in the integrity, interdependence, and 
co-operation of all human interests ? 

1 Science deals with things in the 
abstract, in their isolation, in vacuo. 
Practical life deals with the same 
things in their position in the real 
w wld, surrounded by other things. 

In this distinction lies the value of 
Lotze's definition of the reahty of 
a thing as " a standing in relation," 
vk., to other things, to all things. 
See ' Microcosmus,' book ix. 



Unless I believed that our age was elaborating a deeper is. 
and more significant conception of this unity of all human ?epttono°"' 

• J. i. i» ii • , ^^6 unity 

interests, ot the inner mental life of man and mankind pf^^^an 
I do not think I should have deemed it worth while t^ 
write the following volumes : for it is really their main 
end and principal object to trace the co-operation of many 
agencies in the higher work of our century ; the growing 
conviction that all mental efforts combine together to 
produce and uphold the ideal possessions of our race ; that 
it is not in one special direction nor under one specific 
term that this treasure can be cultivated, but that 
individuals and peoples in their combined international 
life exhibit and perpetuate it. 

A number of words have during this century been in- is. 
troduced by various systems of philosophy to denote this tems for 

., „ , . i.« n expressing 

unity ot the inner hfe of mankind : Hegel's Geist, Comte's *^*^ "^*y- . 
Humanity, Lotze's Microcosm, Spencer's Social Organism, 
all refer to special sides and aspects of the same subject. 
And it is interesting to note how the great schools of 
Idealism in Germany, of Positivism in France, of Evolu- 
tion — physical and mental — in England, and— in spite of 
their apparently disintegrating tendencies — how the social 
changes of the Eevolution and the specialisations of science 
have all combined to emphasise this unity of human life 
and interests. To show this in detail is the object I have 
in view. So far we have not committed ourselves to any 
of the many existing theories : the word Thought seems to i4. 
me to be capable of the widest application, and to denote K^^"^ 
in the most catholic spirit whatever of truth and value 
may be contained in the combined aim and endeavour of 

VOL. I. Q 




1750 to 1S50. 
The age of 
dic treat- 
ment of 

all these modern aspirations. A history of this thought 
will be a definition of Thought itself. 

Much has been done in the course of this century to 
prepare for an undertaking such as the one before me. It 
will be well to review shortly this special side of modern 
literature. We have indeed passed out of what may be 
called the age of encyclopedic treatment of learning— the 
hundred years from the middle of the last to the middle , 
of the present century.* The plan of such an arrangement ■ 
of knowledge belongs to an earlier period, the period im- 
mediately succeeding the birth of modern science. Lord 
Bacon was the father of it, but neither he nor the most 
encyclopisdic inteUect of modern times, Leibniz, did much 
to realise the idea, and it was reserved for the genius and 
the labours of Diderot and d'Alembert'" in France, in the 

1 "Encyclopaedia nomen hodie 
frequentius auditur quam alias." — 
Gessner in Gottinger Lections-Kata- 

log for 1756. 

■^ Diderot's " Prospectus " to the 
* Encyclop^die ' appeared 1750 ; the 
fii-st volume appeared 1751 with the 
celebrated " Discours preliminaire " 
of d'Alembert and a reprint of the 
"Prospectus." The complete title 
was * Encyclopedic ou dictionnaire 
raisonn^ des sciences, des arts et 
metiers, par une soci^t^ de gens de 
lettres, mis en ordre et public par 
Diderot et d'Alembert.' The prm- 
ciples which guided the editors, 
and the object of the work, are ex- 
plained, with repeated references to 
Lord Bacon, in this introduction, 
as well as in the article ♦'Encyclo- 
p6die," m the fifth volume (1755), 
which was written by Diderot, and 
occupied 28 pages. See also Did- 
erot's 'Pens^s sur I'interpretation 
de la Nature,' published anony- 
mously in 1754. 

Copious details about the history, 
the reception, and the influence of 
the ' Encyclopedic ' are to be found 
in the correspondence and memoirs 
of Grimm, d'Alembert, and Vol- 
taire, Madame d'Epinay, the Abb^ 
Morellet, and many others. They 
are combined into a concise narra- 
tive, giving all the important facts, 
in Roseukranz's ' Leben und Werke 
Didcrots,' 2 vols., Leipzig, 1866, 
and in John Morley's 'Diderot. 

It is interesting to note how the 
idea of the unifying and life-giving 
influence of thought was as familiar 
to Diderot as it is to us : " Si Ton 
bannit I'homme ou I'etre pensant 
et contemplateur de dessus la sur- 
face de la terre ; ce spectacle path^- 
tique et sublime de la natun3 u'est 
plus qu'une sc^nc tristc et muettc. 
L'univers se tait ; le silence et la 
nuit s'en em parent. Tout se change 
en une vaste solitude, od les ph^no- 
m^nes inobservds se passent d'une 
manidre obscure et sourde. . . . 



middle of the eighteenth century, to carry out the plan, 
foreshadowed in the 'Novum Organum,' of collecting all 
knowledge, which had been accumulated ever since science 
had been liberated from the fetters of theology, into one 
comprehensive whole. It must, however, be admitted 
that whilst the practical end of these laborious under- 
takings, the dififusion of knowledge, has certainly been 
greatly furthered, the original idea, that the sum of S^e 
human knowledge is an organic whole, has in the exe- fo^t^Sit of 

i • -1 , , in encyclo- 

cution been by degrees entirely lost sight of. The unity 1%%1 
of thought and knowledge was indeed referred to in 
Diderot's " Prospectus " and d'Alembert's " Discours pre- 
liminaire," and in the introduction to Ersch and Gruber's 
great Encyclopaedia,^ as also in Coleridge's celebrated essay 

Voilh ce qui nous a ddtermind h 
chercher dans les facultdsprincipalcs 
de I'homme la division g^ndrale k 
laquelle nous avons subordonnd 
notre travail. "—Article "Encyclo- 
pedic,' p. 641. 

^ Ersch und Gruber's * Allgemeinc 
Encycloptidie der Wissenschaften 
und Kunste,' Leipzig, 1818 to 1875, 
unfinished, 151 vols. It was founded 
by Professor Johann Samuel Ersch, 
librarian at Halle in 1813, assisted 
by Hufeland, Gruber, Meier, and 
Brockhaus, and contained contri- 
butions by the most learned and 
eminent Germans of the century. 
It is interesting to compare the 
plan and principles which guided 
the editors, as expounded in the in- 
troductions to the first and second 
volumes, with the corresponding 
dissertations prefixed to the ' Ency- 
clopedic ' in France and the ' Ency- 
clopaedia Metropolitana' in England. 
The unity aimed at by Bacon was 
either purely formal, securing only 
uniformity and completeness of 
treatment, or it was that of prac- 

tical usefulness— the philosophy of 
fruit and progress. The plan adopt- 
ed by Diderot and d'Alembert could 
hardly attain anything more than 
this. Coleridge, nursed in German 
philosophy, and deeply impressed 
with the fact that there is a higher 
view than that of Lord Bacon, and 
that such is to be found rather in 
writers like Plato and Shakespeare, 
uses the word method in a much 
wider sense. He was deeply affect- 
ed by the spirit of the idealistic 
phUosophy, which was foreign to 
Bacon and unduly despised by him. 
In the idealistic systems of the 
Continent, beginning with Kant, 
the opinion was current that the 
methods and treatment of science 
a!one were insufficient to close the 
circle of knowledge. The truly 
encyclopaedic view, was only possible 
in a scientific investigation speci- 
ally carried on for that purpose, 
and this was considered to be one 
of the main objects of philosophy. 
Thus Kant in many passages of his 
works, notably vol. ii. pp. 377, 378, 




on the science of method prefixed to the ' Encyclopedia 
Metropolitana ' ; but the result has shown, what was not 
evident to Lord Bacon, that neither a systematic division 
of learning according to some logical principle, nor the his- 
torical identity of the beginnings of all branches of know- 
ledge, can in the end preserve the real unity and mtegrity 
of thought. The work of the advancement of learning, 
if it be^'once handed over to different sciences and in- 
trusted to separate labourers, does not proceed in a cycle 
which runs back into itself, but rather in the rings of an 
ever-increasing spiral, receding more and more from the 
common origin. Such is the impression we get if we 
contemplate the unfinished ' rows of Ersch and Gruber ^ 

613 ; vol. iii. pp. 188, 212 ; vol. v. 
p 312 (Rosenkranz's edition), especi- 
aily the two following : " Philos- 
ophy is the only science which can 
procure for us inner satisfaction, 
for she closes the scientific cycle, 
and through her only do the scien- 
ces receive order and connection. 
And: "Mere * iroXvKrropia' is a 
cyclo'pean learning which wants one 
eye— the eye of Philosophy— and 
a' Cyclops among mathematicians, 
historians, naturalists, philologists, 
and linguists, is a scholar who is 
great in all these lines, but having 
these considers all philosophy as 
superfluous." Still, with Kant 
Philosophy is not an "instrument 
for the extension," but merely a 
study of ♦' the limits of knowledge j 
she does not "discover truth, 
but only "prevents error. Ims 
modest definition was given up in 
the systems of Fichte, Schellmg, 
and Hegel, who maintained that a 
certain kind of —and this the highest 
—knowledge could be attained by 
starting from one highest principle 
deductively: the all - embracmg, 
encyclopedic character of philoso- 

phical, speculative knowledge was 
increasingly emphasised, and this 
not only in special lectures on the 
subject, as in Fichte's lectures^ oa 
"The Nature of the Scholar, in. 
Schelling's on "The Method of 
Academic Study," in Hegel's 'Ency-^ 
clopajdia of Philosophy.' but alsa 
in the regeneration and reform of 
many older and in the foundatiott / 
of new universities and academies 
throughout Germany. The great 
* Encyclopeedia ' of Ersch and Gruber 
was planned in a similar spirit, as 
the reform of university teaclung 
and of academic learning. This 
reform has been of the greatest im- 
portance to the German nation and 
to the interests of science and 
knowledge. Tlie Encyclopaedia, on, 
the other hand, has remainedi 
incomplete, a huge but abortive 
attempt to combine not only the- 
principles of knowledge, but also 
the colossal and growing volume of 
it, into a systematic whole. 

1 The promoters of it were evi- 
dently not sufficiently impressed 
with the two very essential con- 
ditions which make a work of this- 


volumes, or if we recognise the fact that the more useful 
and popular publications of our day have abandoned the 
philosophical introductions and preliminary discourses^ 
by which the earlier works preserved a semblance of 
unity and method, and are contented to be merely useful 
dictionaries of reference. The encyclopaedic treatment of 
knowledge, the execution of Lord Bacon's scheme, has 
shown that the extension and application of learning 
leads to the disintegration, not to the unification, of 
knowledge and thought. A conviction of this sort is 
no doubt the reason why in German universities lectures "Encycio- 
on " Encyclopadie " have been abandoned.^ They were aSaidoned 

, , . •'in German 

very general and popular m the earlier years of the ^^^ersities. 
century, when, under the influence of Kant, Fichte, and 


Lectures on 

kind useful— vis., that it must be 
finished, however imperfect it may 
be, and that it must be completed 
within a limited time, on account of 
the revolutions and smaller changes 
in thought and knowledge. These 
essential conditions were always be- 
fore the mind of Diderot. See his 
article "Encyclopedic," pp. 636-644. 
^ The object of the philosophical 
introductions has in course of this 
century been much more completely 
attained by such works as Mill's 
' Logic ' and Jevons's ' Principles of 
Science ' ; whilst the " preliminary 
•dissertations," such as were con- 
tained in the older editions of the 
^Encyclopaedia Britannica,' have 
been partially superseded by works 
like Whewell's 'History' and his 
^Philosophy of the Inductive Sci- 
-euces,' in which the common origin, 
the genesis, the continuous develop- 
ment and interdependence of the 
different sciences, are traced. The 
value in this respect of an under- 
taking like that of the Royal Ba- 

varian Academy (*Geschichte der 
Wissenschaften in Deutschland,' 
vol. i., 1864 ; it has now reached 
22 vols., the science of War signifi- 
cantly filling three large volumes, 
that of Mathematics one small one) 
is much diminished by the title 
suggesting that science is a nation- 
al, not a cosmopolitan or interna- 
tional concern. Fortunately many 
of the contributors to this impor- 
tant and highly useful publication 
have not limited their narratives 
to purely German science, but have 
largely taken notice of non-German 
research. Special reports on the 
state of any science or branch of 
science in a nation have, of course, 
quite a different meaning and 

2 The term is still in use for 
courses of lectures giving a gen- 
eral and comprehensive view of 
special sciences : thus, " Encyclopa- 
die des Rechts, der Medicin, der 
Philologie, der Philosophic, der 


Schleiemacher, university teaching and learning entered 
on a new era, in which the idea prevailed that com- 
pleteness, universality, and unity of knowledge could be 
secured by one and the same arrangement of study, 
was the age when philosophy for the last time had got a 
firm hold of all departments of knowledge, and permeated 
all scientific pursuits ; ^ when, favoured by political events, 

1 On this subject the literature 
connected with the foundation of 
the University of Berlin in the year 
1809 is of special interest. It was 
essentially the creation of Wilhelm 
von Humboldt, though prepared by 
Wolf and Beyme in 1807. See 
Seeley, ' Life of Stein,' vol. ii. p. 
430 sqq. ; Haym, ' Leben \V v. 
Humboldts,' p. 270 sqq. The foun- 
dation of this university m the year 
of Prussia's greatest misery, when 
the first gleams of liberty m the 
rising of Spain and the success of 
Aspern had been extinguished by 
the defeat of Wagram, the voting 
of £22,500 per annum for the pur- 
poses of the new University and 
the Academy of Science and Arts, 
when a crushing war-tax hung over 
the country, when land was depre- 
ciated, the necessaries of life at 
famine prices, the currency of the 
country at a large discount, when 
every one, from the king to the 
lowest subject, was forced into sac- 
rifices and economies of every kind, 
was an act as heroic as the great 
deeds on the battle-field, and as far- 
seeing as the measures of Stein and 
Scharnhorst. Interesting from our 
point of view are the ideas of Fichte 
on university teaching and academic 
learning, laid down in his ' Dedu- 
cirter Plan einer zu Berlin zu ernch- 
tenden hoheren Lehranstalt,' writ- 
ten at the request of the minister 
Beyme in 1807. In it a great deal 
ia said about encyclopaedic treat- 
ment. The question of the position 

of philosophy in the encyclopaedic 
or academic treatment of knowledge 
was easily solved in the Kantian 
school, to which most of the above- 
mentioned writers belonged. Later 
on in the school of Schellmg it be- 
came more difficult. It was fre- 
quently discussed by Schelling him- 
self, who was one of those that 
initiated the new era in the Academy 
of Munich, which was remodelled 
in the year 1807. See, inter aha, 
Schelling's essay, " Suggestions con- 
cerning the Occupation of the Philo- 
logico-Philosophical Class" of the 
Academy, and especially the follow- 
ingremarkablepassage('Werke, vol. 
viii. p. 464 ) : "If, indeed, Philosophy 
were denied living contact with real 
things, if she were obliged to soar 
in transcendent regions without end 
and measure, and to rise a hungry 
guest from the well-appointed table 
of Nature and Art, of History and 
Life ; then it would be incompre- 
hensible how she could still find so 
much support as to be received m 
an academy, and it would be much 
better if we also followed the path 
of other nations, who have lately 
said good-bye to all philosophy, and 
have thrown themselves, with the 
most glowing ardour, upon the ex- 
ploration of Nature and Reality m 
every direction." 

2 The principal representatives of 
the encyclopaedic teaching at the 
German universities were Eschen- 
burg, Krug, and Gruber. The 
latter, in his introduction to the 



ideal aims, a generous spirit of self-sacrifice, and a feeling 
of one common duty pervaded the German nation, and 
foremost in it the teachers and students of the German 
universities.^ This spirit, as it produced co-operation 
and unity of action, also favoured unity of thought, and 
contributed much to the popularity of several philosoph- is. 


ical systems which promised more than they could give, padiasdid 
Encyclopaedic surveys were then supposed to be more ap^p^^red^ 
than the empty shell, the mere skeleton of learning *° p^^^^^^^^- 
which they have since proved to be ; they were looked 
upon as being able to grasp and convey the living spirit 
of knowledge. This phase of thought, which in the 
sequel will largely command our attention, has dis- 

second volume of Ersch and Gruber' s 
' Encyclopiidie,' gives a definition 
and history of encyclopaedic study, 
which, according to him, was intro- 
duced into the modern (German) 
universities together with the philo- 
sophical faculty. In the beginning 
this was subservient to the three 
higher faculties (theology, law, and 
medicine), but gradually took the 
lead. He argues that only since 
university studies have become en- 
cyclopaedic can they be considered 
as furthering true humanity. He 
refers to the great crisis through 
which in the beginning of the cen- 
tury literature, science, and arts 
were passing (p. li), and mentions 
the conflicting principles in the 
treatment of mathematics, physics, 
history, philosophy, and philology. 
See also the * Vorbericht,' vol. i. 
p. vii. 

^ Among the mass of literature 
dealing with this subject, . the 
'Memoirs of Frederick Perthes,' 
by his son (English translation, 
vol. i. chap. xi. sqq.)^ and Steftens's 
* Autobiography ' (' Was ich erlebte,' 

Breslau, 1840-44, 10 vols.), give the 
most vivid and exhaustive accounts. 
Neither Stein, the great statesman, 
nor Goethe, the great poet and 
thinker of the age, took part in this 
alliance of the patriotic and intellec- 
tual interests of the German nation. 
Stein's attitude to the idealism of 
the age is defined by Seeley, * Life 
of Stein ' (vol. i. p. 30, " It is desir- 
able to mark that between him 
and the literature and philosophy 
of his time and country there was 
no connection at all"), and is ex- 
pressed in a remarkable conversa- 
tion which he had with Stefifens, 
March 1813, at Breslau (quoted by 
Seeley, vol. iii. p. 119 ; Stefiens, vol. 
vii. p. 120 sqq. ) Goethe's position is 
defined by his reply to the invitation 
to contribute to the ' Deutsches 
Museum,' a periodical planned by 
the : bookseller Perthes. It was to 
be a scientific alliance of all the in- 
tellect of Germanv, and was in time 
"to be transformed into a polit- 
ical one possessing the strength and 
union necessary for vigorous action " 
(Perthes' Memoirs, vol. i. p. 167). 





appeared; the second half of our century does not 
expect to find the essence of knowledge condensed in 
any philosophical formula, any more than it expects to 
find the real unity and integrity of thought preserved in 
the fragmentary articles of an alphabetical dictionary* 
The purpose of the latter is purely practical; it is a 
popular and handy instrument for the diffusion of 
knowledge, whilst philosophical divisions are merely 
formal, and at best are applicable only to a narrow 
and limited sphere of research.^ 

The age of encyclopaedic representation of learning 
and the short period of philosophical formalism seem 
both to belong to the past ; but the desire of bringing 
together what is scattered, of focussing knowledge and 
learning, and of realising the organic continuity and unity 
of thought and progress, is as great as, perhaps greater 
than ever. Neither the shapelessness of a huge dictionary 
nor the barrenness of a concise formula will satisfy the 

1 It is interesting to observe the 
development and spread of encyclo- 
pfe<lic learning in the three coun- 
tries. Encyclopaedias in the modern 
sense have their origin, like so many 
other modern institutions and ideas, 
in England. They were there com- 
piled mainly for practical purposes. 
France took up the scheme in a 
philosophical spirit, and carried it 
as far as it is capable of being 
carried under this aspect. At- 
tempts to improve and amplify 
the plan proved impracticable ; and 
when subjected to the vast eru- 
dition of Germany, it became evi- 
dent that unity, depth, and breadth 
of view could not be maintained. 
In course of this century the coun- 
try which produced the classical era 

of encyclopaedism has done least for 
encyclopaedic learning. This has 
now its home in Germany, where 
encyclopaedic labours have been 
specialised, and where everj'^ science 
is represented by some compilation 
or annual register aiming at collect- 
ing and systematically arranging the 
scattered contributions of the whole 
world. But it would be ungrateful 
not to mention the Royal Society's 
catalogue of scientific papers, and 
the services which America has ren- 
dered in summarising the literary 
productions of the English-speaking 
nations in such works as Poole's 
* Index to Periodical Literature.' 
Without the aid of such laborious 
compilations the present work could 
not have been undertaken. 

deeper conviction that all mental work is living, indi- 
vidual, and of endless variety. To stimulate individual 
thought, to bring about life and change, is nowadays felt 
to be quite as necessary as to insist on method, system, 
and order. Prompted by this conviction, the last fifty 
years have done much to facilitate intellectual inter- 
change, and to record the historical development of all 
branches of science. 

This object has been promoted in three different ways. 
The French, who in the beginning of the period were the 19. 
masters in science, led the way by founding a series of the masters 

in science 

periodicals devoted to the development of separate sciences, t^ *^® . 

•*■ JT jr begmni 

Germany followed, and still later England.^ A living °^ ^^'® ^^" 

of the 

^ The oldest scientific periodical 
is the ' Journal des Savants,' which 
was started in 1665 in Paris; next 
to it comes probably Rozier's * Ob- 
servations sur la Physique' (1771), 
continued under the title 'Journal 
de Physique ' (1778, continued with 
interruptions from 1794 - 95 till 
1823). In opposition to this 
journal, which defended the older 
phlogistic theories in chemistry, 
the ' Annales de Chimie ' were 
started in 1789 by BerthoUet, 
Guyton de Morveau, and Fourcroy, 
as an organ of Lavoisier's ideas. 
In 1788 the Society Philomatique 
started its * Bulletin,' and in 1795 
the * Journal de I'Ecole Poly- 
technique' started its influential 
career. No such periodicals existed 
for special sciences at that time in 
any other country, if we perhaps 
except the * Transactions of the 
Royal Linnaean Society,' which 
started in 1791. * Nicholson's 
Journal' started in 1797 ; the 
'London, Edinburgh, and Dublin 
Philosophical Magazine and Journal 
of Sciences ' had its origin in Til- 
loch's * Philosophical Magazine' ; but 

the first journal devoted specially 
to mathematical sciences in England 
was probably the 'Cambridge Ma- 
thematical Journal,' started in 1839. 
In the meantime the number of 
scientific journals in France had 
grown enormously. In Germany we 
have Crell's ' Chemische Annalen ' 
(1778), Gehlen's 'Allgemeines Jour- 
nal fiir Chemie' (1803), Gren's 
'Journal der Physik' (1790), Gil- 
bert's ' Annalen der Physik' (1799), 
Zach's 'Monatliche Correspondenz ' 
(1800), Crelle's 'Journal fiir die 
reine und augewandte Mathematik' 
(1826), and many others, all peri- 
odicals of the first imoortance. The 
* Transactions of the Royal Society,' 
which of course contain many of 
the valuable scientific contributions 
of this country, can nevertheless 
hardly be looked upon as a reposi- 
tory of the work of English mathe- 
maticians and physicists of the 
period in question, — not even as 
much as the Memoirs of the Paris 
Academy in France. In Great 
Britain a new centre of scientific 
and literary work existed during 
the latter part of the last century 






intercourse between men of science was greatly promoted 
by the British Association for the Advancement of Science, 
which held its first meeting at York in 1831. Associa- 
tions and meetings of this kind had their origin ten years 
earlier in Germany through Oken ; ^ but the line in which 
Germany has done most is the establishing of and con- 
tinuing annual Keports ^ of the progress of the different 

in Edinburgh (* Transactions of the 
Royal Society of Edinburgh,' started 
in 1788), and somewhat later like- 
wise in I)ublin (' Transactions of the 
Royal Society of Dublin,' started 
1799), and Manchester ('Memoirs 
of the Manchester Philosophical 
Society,' started in 1789). Many 
of the first scientific writers of the 
age published in these provincial 
papers or in separate pamphlets — 
the want of a common collecting 
centre being very obvious. 

^ Alexander v. Humboldt sup- 
ported them, and was instrumental 
ill giving to the Assembly at Berlin 
in 1828— which he called "The in- 
vasion of philosophers " — a special 
importance. It was, as he says, 
" a noble manifestation of scientific 
union in Germany ; it presents the 
spectacle of a nation divided in 
politics and religion, revealing its 
nationality in the realm of intellec- 
tual progress." — Bruhns, 'Life of 
A. V. Humboldt,' vol. ii. p. 130. 
The British Association for the Ad- 
vancement of Science was (as Prof. 
Owen informs us) at the outset 
avowedly organised after the Oken- 
ian model. — 'Encyclopaedia Britan- 
nica,' art. "Oken." 

2 The first reports aiming at 
giving a statement of the position 
of Science were those drawn up by 
Delambre and Cuvier at the request 
of the Emperor Napoleon I., and 
presented in the year 1808 under 
the title ' Discours sur les Progrfes 
des Sciences, Lettres, et Arts depuis 

1789 jusqu'h ce jour ' (1808). They 
were imitated on a larger scale by 
the Emperor Napoleon III., on the 
occasion of the great Paris Exhibi- 
tion 1867, and have been continued 
under the Republic. Of the report 
of 1808 Cuvier says, "Ce tableau 
historique nous servira desormais 
de point de depart et nos rapports 
annuels en seront autant de con- 
tinuations." He also adds signifi- 
cantly, " Dans les relations actives 
oh nous nous trouvons avec la 
plupart de ceux qui cultivent les 
sciences, il est bien difficile qu'ils se 
f assent en Europe quelques d^cou- 
vertes importantes sans que le 
bruit en retentisse promptement 
dans cette enceinte, et nous excite 
h des travaux qui s'y rapportent 
plus ou moins directement. " 

By far the most important work 
of reporting and summarising the 
results of scientific labour has been 
done by Germany. The first publi- 
cation of this kind, however, origin- 
ated with Berzelius, who from the 
year 1821 reported regularly to the 
Academy of Stockholm on the pro- 
gress of the physical sciences. Of 
Berzelius's periodical Kopp says 
('Geschichte der Chemie,' vol. i. p. 
403), that it " summarises with the 
greatest completeness all that had 
been done in chemistry since 1820.'* 
This work, which regularly ap- 
peared in German translation, was 
continued in Liebig's * Jahresbericht 
der Chemie' (1847). In Berlin the 
* Physikalische Gesellschaft ' hsks 

sciences, in which all scientific researches are — without 
regard to nationality — reviewed, classified, and arranged in 
the most complete manner, according to the place which 
they occupy in the general development. Invaluable ser- 
vice has also been done in England by special Eeports or 
Addresses, prepared by men of the greatest eminence — fre- 
quently at the request of the British Association — in which 
the position of special branches of science is explained, the 
work of the past summed up, the leading principles clearly 
brought out, and the unsolved problems placed promi- 
nently before the minds of young and aspiring workers. 

In Germany during the first half of the century a 
reaction set in against the metaphysical treatment of i^^'oermany 

against me- 

scientific subjects, which had been exaggerated in the SStmeS! 
schools of Schelling and Hegel. Experimental research, subS'^'' 
following mainly the great French and English models, 
was next favoured, and through the establishment of 
laboratories and observatories, through voyages of dis- 
covery and the application of science to the industries, 
an enormous amount of detailed and minute knowledge 
was accumulated.^ For a time — even within the limits 


continued to issue regularly since 
1845 annual Reports under the title 
' Fortschritte der Physik.' But it 
was only in 1868 that a similar 
annual was started in Berlin having 
reference to mathematics, under 
the title ' Fortschritte der Mathe- 
matik.' A 'Jahresbericht' on 
Zoology has appeared ever since 
1879, and one on Botany since 1873. 
^ It was the age which compiled 
the great repositories of chemical 
knowledge. Such were Gmelin's 
* Handbuch der Chemie' (1st ed., 
1817. Translated into English by 

the Cavendish Society, 1848), and 
the ' Handworterbuch der reinen 
und angewandten Chemie' (edited 
by Liebig jointly with Poggendorf 
and Wohler, 1837). The same age 
also set going and filled the volumes 
of Liebig's ' Annalen ' (started by 
Hanle in 1823 under the title 
'Magazin der Pharmacie,' it finally 
assumed the title of 'Annalen der 
Chemie und Pharmacie ' under Lie- 
big's editorship), of Poggendorfs 
* Annalen der Physik und Chemie ' 
(1824), and the ' Annales de Chimie 
et de Physique.' 



of exact reasoning — attempts to condense and unify 
knowledge were discredited. The result — especially in 
Germany — was that in many sciences information be- 
came buried in periodicals and in the memoirs of learned 
societies: text -books were chiefly written by men of 
secondary importance, translated from the French and 
English, and frequently on somewhat antiquated lines.^ 
The new spirit which began to leaven scientific research in 
the middle of the century was confined to a few master 
minds, who — frequently almost unknown — marched in 
advance of their age. In the course of the last thirty 
years this has been entirely changed. The means of 
intercourse and communication, referred to above, make 
scientific isolation almost impossible ; the necessity has 
21. been felt of remodelling the whole of the popular school 

Reform in 

school litera- literature on more modern lines : some of the first m- 


^ The greater part of the higher 
Germau school literature in mathe- 
matics and phj'sics was supplied by 
the French or modelled on French 
ideas — Legendre and Monge in ele- 
mentary and descriptive geometry, 
Lacroix in the higher branches. 
Francoeur's course of mathematics 
was introduced in England as well 
as Germany ; Poisson, and later 
Lagrange and Duhamel, became 
the models in mechanics, Biot and 
Pouillet in experimental physics, 
Regnault in chemistry. The only 
great popular authorities which 
did not belong to France were 
Berzelius and Graham in chem- 
istry, and Euler in mathematics. 
As late as 1860 hardly any text- 
book existed in Germany on the 
theoretical and mathematical por- 
tions of physics. The second 
volume of ' Baumgartner ' was 
a miserable compilation. Beer's 
* Hohere Optik ' was the first im- 

portant work of this kind. Ger- 
many had indeed not been wanting 
in original research, but the new 
ideas of Mobius, Steiner, Staudt, 
Pliicker, and Grassmann in geom- 
etry found no adherents till, mainly 
through the translation of Sal- 
mon's text-books by Fiedler, a new 
spirit came over geometrical teach- 
ing. In the meantime Lejeune 
Dirichlet, and Neumann the elder, 
cultivated in their academical lec- 
tures the higher branches of mathe- 
matical physics, and educated a 
whole generation of mathematicians 
and physicists. Through them the 
original researches of Gauss and 
Jacobi became better known, and 
an independent school of German 
mathematical thought was estab- 
lished. In England the influence 
of French science was much more 
limited, and to the present day 
Euclid is preferred to Legendre's 
more elegant methods. 



tellects in science have condescended to write text-books 
of their subjects, by which a great reform has been brought 
about in the higher scientific literature.^ At the same time 
— after fifty years of experimental research and accumula- 
tion of material — it has become necessary to review the 
fundamental principles on which scientific reasoning rests : 22. 
a more philosophical, not to say metaphysical, spirit is Ssonlng 
manifesting itself within the limits of science.^ In the ^opuSi!'" 
abstract, and especially the mathematical, sciences, real 
progress depends now mainly upon the discovery of 
methods of simplification, on conciseness and elegance 
of treatment, and on the discovery of unifying principles 
and generalising aspects.^ 

^ This remark refers mainly to 
England and Germany. In France, 
as a result of giving lectures at the 
Ecole Polytechnique, the Bureau 
des Longitudes, the Faculte des 
Sciences, &c., the great mathema- 
ticians and physicists of the cen- 
tury have frequently worked up their 
researches in connected treatises. 
For such we are indebted to Lamd, 
Cauchy, Poncelet, and many others. 
But the two works which in Eng- 
land and Germany created probably 
the greatest reform in the teaching 
of the principles of natural phil- 
osophy were Thomson and Tait's 
' Natural Philosophy ' (first sketch, 
1863, Isted., 1867) and Kirchhoff's 
' Vorlesungen uber Mechanik' (Leip- 
zig, 1877). 

'^ I refer principally to the various 
writings of Helmholtz, following 
those of Riemann, and the many 
hints thrown out in Gauss's pub- 
lished papers, and in his correspond- 
ence with Schumacher. Helmholtz 
has— of all purely scientific writers 
— paid most attention to the meta- 
physical foundations of geometry 

and dynamics, and has critically 
examined the earlier theories of 
Kant, published a century ago. It 
is interesting in this respect to note 
what Kant is reported to have said 
to Stiigemann in 1797: "I have 
come with my writings a century 
too soon ; after a hundred years 
people will begin to understand me 
rightly, and will then study my 
books anew and appreciate them.'* 
(See ' Tagebiicher,' von Varnhagen 
von Ense, Leipzig, 1861, vol. i. p. 
46.) Next to Helmholtz we are 
most indebted to Emil du Bois- 
Reymond and his brother Paul. 
See Emil's 'Reden' (Leipzig, 1886- 
87, 2 vols.), and the posthumous 
work of his brother : * Ueber die 
Grundlagen der Erkenntniss in den 
exacten Wissenschaften ' (Tubingen. 
1890). ^ 

^ An authority on this subject 
says: "Generality of aspects and 
methods, precision and elegance 
of exposition, have, since the time 
of Lagrange, become the common 
property of those who claim to 
be scientific mathematicians. This 




has taken 
the lead in 
the life of 

All these are merely external signs of the new life, in- 
dications of progress and change : the inner reason and 
result, the altered ways of thinking which underlie or are 
produced by these external changes, will be the object 
of closer study hereafter ; they constitute the real sub- 
stance of this work. What I draw attention to here, 
by way of introduction, are merely fingers on the dial- 
plate of a complicated clock-work : their motion and posi- 
tion are patent to every one. Later on I shall invite the 
reader to remove the outer case, and try with me to under- 
stand the delicate working parts and the principle of the 
mechanism, the prime mover and the mode of transmission 
of motion within. The general curiosity that exists to fol- 
low the internal and hidden workings of thought is mani- 
fested especially in that country which in modern history 
has frequently taken the lead in philosophical reasoning. 
It is manifested by the huge and increasing historical 
literature of Germany, which is devoted to tracing out 
the growth and development of modern science and 
thought. In that country history seems for the moment 
to have taken the place of metaphysical speculation. 
A similar transition from the logical to the historical view 
can be traced in English literature in the last century, the 

generality is sometimes exaggerated 
at the expense of simplicity and 
usefulness, and then leads to ab- 
struseness and to the enunciation 
of theorems which have no special 
application ; precision may degen- 
erate into an affected brevity which 
renders a dissertation more difficult 
to read than to write ; elegance of 
form has in our days almost be- 
<;ome the test of the value of a 
theorem. Yet in spite of all draw- 

backs these conditions of efficient 
progress are of the greatest import- 
ance, inasmuch as they keep the 
scientific matter within those limits 
which are intrinsically necessary if 
mathematical research is not to lose 
itself in minutiae or be drowned in 
over - abundance." — Hankel, ' Die 
Entwickelung der Mathematik in 
den letzten Jahrhunderten ' (Tiib- 
ingen, 1869). 



typical representative of that change being David Hume, 
who, starting with the metaphysical problems involved in 
Locke's and Berkeley's writings, was from them led on to 
the study of moral, political, and economic questions, and 
ended by devoting himself to the study of history.^ At 
the end of his career pohtical and historical writings 
were as frequent in English literature as metaphysical 
and theological writings had been at the beginning. The 
causes which have effected the same transition from the 24. 
metaphysical to the historical mode of treatment in Ger- SSon 

YVA J • J.^ from meta- 

many durmg the present century are similar to those g^Si^'' 
existing in England in the last century ; but the whole "''^^'^ 
movement has taken place on a larger scale, penetrates 
deeper into the mental life and work of the nation, and 
cannot be so easily studied in the writings of any great 

Whilst in Germany historical studies are now foremost, 

^ I am quite aware that general- 
isations of this kind must be made 
and used with great caution. I 
therefore refer my readers to Les- 
lie Stephen's 'History of English 
Thought in the Eighteenth Cen- 
tury,' especially to the Introduc- 
tion, where the typical position of 
Hume is fully discussed, and also 
to the last chapter of the second 
volume, where he says of Hume 
<vol. ii. p. 381, 1st ed.) : " Hume was, 
in one sense, far in advance of his 
time, and indeed of the average 
opinion of the present time. But 
the change may in many respects 
be described as a revolt from 
Hume's opinions, much more than 
a development of them. . . . The 
history of philosophical and of theo- 
logical opinion in England is a his- 
tory of gradual decay down to the 

revolutionary era." And p. 444: 
" The last half of the century was 
pre-eminently historical. As civil- 
isation progresses, as records are 
better preserved, and a greater 
permanence in social organisation 
makes men more disposed to look 
beyond their immediate surround- 
ings, a tendency to historical in- 
quiry is naturally awakened. This 
cause alone, without the more 
philosophical considerations which 
might lead a Hume or a Gibbon 
to turn from abstract investigations 
to historical inquiries, may account 
for the growth of antiquarianism in 
the latter years." But the mere 
statistics of English literature in 
the eighteenth century suffice to 
prove the decline of argumenta- 
tive and the growth of realistic 




Spencer the 
first Eng- 
lishman who 
has pro- 
duced a 
system of 

of Lotze's 

and have almost dislodged systematic philosophy, England 
has for the first time in her history produced a system of 
philosophy — that of Mr Herbert Spencer ; and this with 
the distinct understanding that the object of philosophy 
is the unification of knowledge.^ It is a remarkable fact, 
which will occupy our close attention hereafter, that the 
unifying principle in this system is historical, — a process 
of development now specially known under the term 
Evolution. This system forms in a certain way a con- 
trast to the last great system in German philosophy, that 
of Hermann Lotze. Whereas in all systems of evolution 
the unity of things is historical, and has to be sought in 
their common origin, Lotze emphasised the truth that 
unity must be a living presence, a principle which ex- 
ists in individual things, not merely a link which con- 
nects them by proximity in time or space. His object 
is to answer the question. How can the human mind , 
represent to itself such a living unity, in what ideas 

^ See G. H. Lewes ('Problems 
of Life and Mind,' Ist ed., vol. i. 
p. 84), who says : " The absence 
of a philosophy in England dur- 
ing the last two hundred years 
has been a serious defect in her 
culture. Science she has had, 
and poetry aqd literature, rivalling 
when not surpassing those of other 
nations. But a philosophy she has 
not had, in spite of philosophic 
thinkers of epoch-making power. 
Hobbes, Locke, Berkeley, Hume, 
have produced essays, not systems. 
There has been no noteworthy at- 
tempt to give a conception of the 
world, of man, and of society, 
wrought out with systematic har- 
monising of principles. There has 
not been an efifort to systematise 
the scattered labours of . isolated 

thinkers. Mr Herbert Spencer is 
now for the firat time deliberately 
making the attempt to found a 
philosophy." And in his * History 
of Philosophy ' (3rd ed., vol. ii. p. 
653) the same author says : * ' Mr 
Spencer alone of British thinkers 
has organised a system of philos- 
ophy." Groom Robertson would 
take exception to this in favour 
of Hobbes, " who attempted a task 
which no other adherent of the 
' mechanical philosophy ' conceived 
— nothing less than such a univer- 
sal construction of human know- 
ledge as would bring Society and 
Man within the same principles of 
scientific explanation as were found 
applicable to the world of Nature '* 
(Ency. Brit., 9th ed., vol. xii. p» 


belonging to human thought can this unity be grasped 
by what words of human speech can it be expressed ? ' 
Both Mr Herbert Spencer's 'System' and Lotze's ^Micro- 
cosmus ' are written with the object of establishing the 
umty of thought, of preserving the conviction that things 
exist and that events happen in some intelligible connec- 
tion, and especially that the religious and the scientific 
views of the world and life are reconcilable. But whereas 
Mr Spencer is content to point to the underlying unity as 
the Unknowable, and then betakes himself to the study 
and exposition of the manner in which events foUow and 
things develop, Lotze considers the whole of this part of 
philosophy as merely an introduction to the solution of 
the real problem. To him a process of development is 
merely the outer form in which some real substance pre- 
sents Itself, a mechanical method by which something of 
. higher value is accomplished. He admits the all-pervad- 
mg rule of such a mechanism, but he urges the necessity 
of finding the substance itself, and of gaining a view of 
the end and aim which is to be attained by this array of 
processes, by this parade of mechanical means, of the in- 
terest that attaches to them, and the result which is to be 
secured.^ Knowing the mechanism by which a certain 
object IS accomplished, we may be able to calculate pheno- 
mena and events, but to understand ^ them requires a 

The earliest passage in which 
Lotze gives us a pretty complete 
idea of his philosophical methods 
and aims is to be found in his pol- 
emical pamphlet against Fichte the 
younger ('Streitschriften,' Leipzig, 
1857, p. 52 sqq.) He there also 
reviews his attitude to the ideal- 
istic school of German Philosophy 


and to Herbart, whose follower he 
refuses to be called [ibid., p. 5 so ) 
It IS evident that at that time his 
system was not yet definitely set- 
tled m his mind (p. 58). 

'-^ The difference between calcula- 
tmg and understanding phenomena 
IS probably to be traced to Leibniz. 
Lotze emphasises this difference. 


Lotze's re- 
lation to 


further knowledge of the worth of the object which is 
accomplished, of the result which is gained by the calcu- 
lation. It is one thing to be able to trace the mechanical 
conditions upon which the accuracy of a clock depends ; 
it is another to mark the hour which. the clock strikes, 
and to note the time which it measures out to us for our 
work. Curiosity will lead a child to pry into the former ; 
but the latter depends on our appreciation of the objects 
of life and the seriousness of our duties. 

When Lotze undertook to write the ' Microcosmus/ he 
referred to two great works of a kindred tendency. Both 
attempted, yet in very different ways, to give a compre- 
hensive view of a large field of scattered phenomena, to 
take in at a glance the entire scheme of a great world of 
facts The earlier of the two belonged to the last century 
and was concerned with history, with the uniting bond of 
all human development. For this Herder, in his ' Ideen 
zur Philosophie der Geschichte der Menschheit,' had, if not 
invented, yet endowed the term Humanity with a specific 
pregnancy, meaning by it the unity of all human interests 
in their social and historical development— an idea which 
since Leibniz has governed German literature.^ The other 

See, inter alia, the closing para- 
graph of the first volume of the 
' System der Philosophie ' (Ist ed. , 
Leipzig, 1874). I cannot omit to 
notice here the extraordinary and 
misleading misprint in Erdmann s 
quotation of this passage : see his 
valuable 'Geschichte der Philoso- 
phie' (3rd ed., Berlin, 1878, vol. u. 
p. 861), where instead of berechnen, 
to calculate, we read bezeichnen, to 
designate ! 

1 The history of this idea has 
been written by Hettner in the 

last two volumes of his * Literatur- 
geschichte des 18 ten Jahrhunderts. 
I quote from the 2nd edition, 
Braunschweig, 1872. Herder had 
inherited the spirit of Leibniz (see, 
inter alia, the concluding chapter 
of my essay on Leibniz, in Black- 
wood's Philosophical Classics, Edin- 
burgh, 1884). Herder formed a 
kind of centre of thought, inas- 
much as he gathered up in his own 
mind and writings the influences of 
Leibniz, Rousseau, and the Eng- 
lish writers of the eighteenth cen- 



great work was that of A. v. Humboldt, who in the course 28. 
of a long career, peculiarly favoured by opportunities for Sn to" 
studying Nature on an extensive scale, and for appreciating JxJidt's '™' 
the detail of modern research, of which he was an illustrious 
representative, had never lost sight of the all-pervading 
unity.^ In an elevated style, in which poetry and science 

tury, together with classical influ- 
ences and new inspirations drawn 
from the popular song-literature of 
all nations. Hettner says (see last 
volume but one, p. 7) : " Herder 
applied Rousseau's gospel of Nature 
to the demands of poetical sense 
and creation. Thus he has become 
essentially the forerunner of the 
new school of poets : the last fetters 
of the moralising style by which 
even Lessing was still hampered 
fell, and through the scientific study 
of the beginnings and development 
of human culture he became the 
founder of a new science of Lan- 
guage, Religion, and History, in the 
lines of which we are still advanc- 
ing." And p. 101 : " Herder does 
not belong to the classics of the 
style of Winckelmann, Lessing, 
Kant, Goethe, and Schiller ; he is 
everywhere only suggestive, hardly 
anywhere conclusive and final. For 
this reason his writings are to some 
extent antiquated. Nevertheless 
Herder is one of our most im- 
portant and influential spiritual 
heroes. Herder made so deep an 
impression on his age that the 
great poetry of Goethe and Schiller, 
the so-called Romantic School, the 
philosophies of Schelling and Hegel, 
cannot be imagined without Herder 
as the precursor." The fourth 
volume of Gervinus, 'Geschichte 
der deutschen Dichtung,' contains 
likewise a very important chapter 
on Herder. But the great authority 
on Herder is R. Haym, ' Herder nach 
seinem Leben und seinen V7erken ' t 
(Berlin, 2 vols., 1880 and 1885). I 

From the unpublished literary 
notes, correspondences, and diaries 
of Herder, which Haym inspected, 
it is evident that the great idea of 
writing a History of Humanity 
originated in Herder's mind as far 
back as the year 1769, on a voyage 
from Riga to Nantes (on the way 
[ to Paris). His diary closes thus : 
" History of the progress and of the 
powers of the human mind in the 
concurrence of whole ages and 
nations — a spirit, a good demon, has 
exhorted me to do this. Be that 
my life's work, History, work !" 

The first attempt to carry out 
his great idea was published by 
Herder in the year 1774, with the 
title : ' Auch eine Philosophie der 
Geschichte zur Bildung der Mensch- 
heit.' Herder was then in his 
thirtieth year. His chief work 
appeared ten years later (1784), with 
the title * Ideen zur Geschichte der 
Menschheit.' Herder died in 1803. 
Goethe's 'Faust,' which is an at- 
tempt to deal with the highest 
problems of human interest, the 
problems of knowledge, evil, sin, 
and redemption, as they appear in 
the history of a great individual, 
not of the race, had its first begin- 
nings about the same time as Her- 
der's 'History of Mankind.' But 
the work was not finished till a year 
before Goethe's death in 1831. 

1 Alex. V. Humboldt, ' Kosmos. 
Entwurf einer physischen Welt- 
beschreibung,' 1845. Like Her- 
der's great work on the ' History of 
Humanity' and Goethe's 'Faust,' 
Humboldt's ' Kosmos ' occupied a 


I/otie's 'Mi 


are happily blended, he essayed in the evening of life to 
unroll before the gaze of his readers a picture of the 
grand features of nature as his mind had viewed them 
Lm the elevated regions of scientific study, and his eyes 
from the heights of Chimborazo. ■ 

In the great picture of the world, in the vaBt changes 
of the universe, where is man with his life and his m- 
terests ? In the huge Kosmos where is the Microcosmus 
This question naturally presented itself to the mind of 
Lotze. " It is not," he tells us, " the all-embracing kos- 
mos' of the univei^e which we wish to describe agam on 
the model which has been given to our nation. As the 
features of that great world -portrait sink deeper into 
general consciousness, so much more vividly will they 
lead us back to our own selves, suggesting anew the 
question. What significance belongs to man and human 
lie with its lasting characteristics and the changing 





i » 

long period in the life of its author. 
Goethe's * Faust ' deals with the in- 
dividual problem, Herder's Ideen 
with the problem of the race or 
mankind. Humboldt's 'Kosmos 
with the same problem as referring 
to the worid, the universe. In the 
preface Humboldt confesses that 
The image of his work had stood 
before his mind's eye m undefined 
outlines for nearly half a century : 
cf. what Goethe says in the dedica- 
tion to * Faust' (written probably 
after 1797) :— 

"Again ye come, ye hovering forms; I 
As eariy to my clouded sight ye shone," 

^^' -Transl. B. Taylor. 

The view of the universe which was 
eiven in Humboldt's ' Kosmos was 
prepared by his own pubhcation, 

» Die Ansichten der ^a^ur (1808) ; 
also by Georg Forster (1/54-1/94), 
who wrote an account of the second 
voyage of Captain Cook round the 
world, whom he accompanied with 
his father. " He conceived of na- 
ture as a living whole ; his account 
is almost the first example of the 
glowing yet faithful description of 
natural phenomena, which has since 
made the knowledge of them the 
common property of the educated 
worid " (R. Garnett in ' Ency. Bnt., 
art. "Forster"). Humboldt con- 
fesses to have received from him 
"die lebhafteste Anregung zu wei- 
ten Unternehmungen " (' Kosmos, 
vol. i. p. 345, also vol. ii. p. 65, and 
especially vol. ii. p. 72 where m- 
cidentally also Darwin s narrative 
of the " Adventure " and " Beagle 
is mentioned). 

course of its history in the great totality of nature ? " ^ 
And in collecting the answers to this, question which 
suggest themselves both in and outside of the study, 
Lotze professes only to renew the enterprise brilliantly 
begun by Herder in his 'Ideen zur Geschichte der 
Menschheit.' Both Herder's 'Ideen' and Humboldt's 
' Kosmos ' belong to the age in which philosophy and 
poetry largely influenced science and history. Many may 
now think it premature or altogether impossible to try 
to combine the detailed studies of modern science and 
modern history with the comprehensive view demanded 
by philosophers and poets, or to grope through the laby- 
rinth of external phenomena and events to their under- 
lying significance and unity. They may, whilst fully 
maintaining the existence of an all -pervading power, 
nevertheless relegate it with Mr Spencer to the region 
of the Unknowable.^ Without desiring at present to 

^ Microcosmus, Ist ed., Leipzig, 
1856, Preface. Hermann Lotze was 
born in 1817, and died in 1881. 
His first philosophical essay of im- 
portance was the ' Metaphysik ' 
(Leipzig, 1841). 

- Herbert Spencer's Philosophy 
of the " Unknowable " is laid down 
in his Introduction to * First Prin- 
ciples.' I believe the first appear- 
ance of the first part of this book 
was in 1860, and the first collected 
publication in the year 1867. In 
■defining the region of the Know- 
able an opposite course has been 
adopted by Emil du Bois-Reymond, 
who in a series of addresses and 
articles, now collected in two vol- 
umes with the title 'Reden' (Ber- 
lin, 1886 and 1887), tried to lead 
up to the limits which are fixed 
around scientific knowledge. The 
purport of his teaching on the 

highest " World -problem " is con- 
tained in the four words, ignoramus, 
ignorabimus, dubitcmus, laboremus. 
"The first of these addresses, which 
are full of brilliant suggestions and 
vivid illustrations, furnishing in the 
notes especially an invaluable store 
of historical references on the sub- 
ject of the philosophy of the sci- 
ences, was delivered at the forty - 
fifth meeting of the German "Na- 
turforscher und Aertze," and pub- 
lished at Leipzig, August 1872, with 
the title ' Die Grenzen des Natur- 
erkennens.' It made a great sensa- 
tion, and was translated inte several 
languages. It was followed some 
years later by an address delivered 
in the Berlin Academy, 1880, and 
published with the title * Die sieben 
Weltrjithsel. ' If H. Spencer's phil- 
osophy is termed the philosophy- 
of the Unknowable, Du Boir^aKSy 


criticise the weighty considerations which have led them 
to a view so modest and resigned, I propose m the 
sequel to test within narrower limits, and by what 
seems to me a novel method, the validity of the con- 
viction that a true understanding of phenomena and 
events can be attained only by viewing them m their 
interdependence and collective effect. If anythmg m 
the wide expanse of physical and mental life deserves 
to be considered as one and indivisible, it is surely 
human thought in its various branches and manifesta- 
tions. The attempt to trace its origin in the early ages 
of civilisation, or to foreshadow the end which it is 
slowly approaching, may indeed be impossible ; but of 
the age to which we belong, and the literature of 
which we have witnessed the growth, we may claim to 
possess a deeper knowledge. Astronomers have sue 
ceeded in gaining a view of immense and distant orbits 
by minutely observing and tracing merely an insignifi- 
cant portion^ which came within their view. Com- 
. parative anatomy teaches how from a few survmng 
links to construct the whole framework of an orgamsm. 
I propose to apply a similar method to the small portion 



mond's may be termed the philo- 
sophy of the Limits of the Know- 
able. Both views form a contrast 
to Lotze's philosophy. 

1 The most brilliant example of 
this is the discovery of the planet 
Ceres by Piazzi at Palermo m the 
New Year's night of 1801 ; the in- 
vention of special methods for cal- 
culating the orbit of this planet, 
which had been lost, by Gauss in the 
course of 1801; and the rediscovery- 
>f it by Olbers, aided by Gauss s 
'^ jmeris, in the New Year's night 

of 1802. After the discovery of this 
first of the small planets, but before 
it was known in Germany, Hegel 
published his 'Dissertatio philo- 
Bophica de orbitis planetarum,' m 
which he ridiculed the search for 
new planets, but which Duke Ern- 
est of Gotha sent to the astrono- 
mer Zach with the superscription, 
"Monumentum insanise sseculi de- 
cimi noni." See R. Wolf, Ge- 
schichte der Astronomic, Miinchen, 
1877, p. 684 iqq. 

of mental progress of which I have been able to take 
personal notice and of which I have felt the immediate 
personal influence. A tracing as concisely as possible 
of this comparatively small portion of the course of 
European thought may be the first approximation to 
more accurate delineations, which themselves will be 
the means of gradually gaining a truer idea of the pur- 
port and significance that belong to the larger dimen- 
sions of the mental life of mankind. 

This life does not consist in the accumulated knowledge 
of our century, not in the results of scientific inquiry de- 
posited in libraries and museums, not in the many schools 
for learning and study, not in educational and social re- 
forms, least of all in political and economic institutions. 
These are all external objects, which are capable of being 
described or photographed like the external objects of 
nature. The mental life of mankind consists in the inner so. 

What the 

processes of reflection, by which these external objects have S^in^nVr^d 
been produced, by which man has been able to add to the ^'^^^^^^^o^- 
physical creation of nature a new creation of his own, by 
which he has been able to change the face of the earth, 
and endow the objects of nature with an ideal meaning. 
To this end he is always inventing and using methods 
which change, suggesting and applying principles which 
turn out to be half true or totally fallacious, guessing at 
results and aims which have to be abandoned, inventing 
theories which are short-lived — in fact, erecting scaffold- 
ings with the help of which he raises the structures of 
Society, Art, and Science : these remain as the historical 
testimonies of his activity ; the scaffoldings are removed as 
of merely transient and temporary value ; and yet they 






the most 
have their 
day, and 
cease to be. 

One centnry 
does not 
inherit all 
of the past ; 
it discards 

alone constitute the mental life which interests us. Only 
so far as we have taken part in building the scaffolding, 
only in so far as we have witnessed the many contrivances 
which have been used, only in so far as we have seen the 
growth of any structure from small beginnings, from the 
first sketch of the architect, can we say that we know 
something of the mental life which lies hidden in and 
behind those external signs and documents. A closer 
study of what we ourselves have witnessed is thus the 
only way of attaining some insight into the workings of 
the mind — the spiritual life of mankind. We shall pres- 
ently find that in science as well as in philosophy every 
period starts from certain assumptions and proceeds ac- 
cording to certain methods, that certain habits of thought 
become general, and certain views become accepted ; but in 
the course of one or two generations we find those assump- 
tions questioned, those methods criticised, a new habit of 
thought introduced, and those general views which seemed 
so natural and convenient giving way to new and altered 
ones. The whole fabric of society, the whole structure of 
science and knowledge, all the applications of art, have to 
be remodelled on new principles, and to meet our changed 
demands. Few indeed, very few, of the old creations 
remain. One or two so-called laws of science that sur- 
vive, a few dozen books that are re-edited, half-a-dozen 
works of art and one or two great poems, — this is about 
all that our century will at its close have preserved as the 
living inheritance of its early years : all the others will be 
relegated to the growing bulk of historical records. Pos- 
sessed of merely monumental interest as documents of a 
bygone life, these creations had to be left aside as incap- 

able of marking or guiding any longer our onward career. 
A few centuries lapse, and posterity will look upon thena 
as we do on the huge monuments of early Eastern civili- 
sation, on the Sphinx in the desert pr the Pyramids of 
Egypt, wondering by what ingenious contrivances they 
were raised, what amount of human work and suffering 
they represent, or what idea lived in the minds of those 
who planned and placed them where they still remain. 


It is the privilege of art to represent at a glance the , 
whole of Its object, and thus to produce at once a total Sf/ 
effect on the mind of the beholder. Closer scrutiny may "^'■ 
follow and may show how the various parts support 
the whole, how the uniting idea is revealed in all the 
mamfold detail of the component elements : still the im- 
pression of the whole remains and supplies the key for 
the comprehension of every part. Literature, science, and 
history are denied this privilege of presenting their ob- 
jects m their entirety, and thus giving from the outset a 
commanding view, a leading and abiding impression of the 
whole. We have to ask the student to follow us patiently 
by an isolated path to the summit : many ways lead to it 
and we may err in the choice of the right and convenient 
one. Even if we succeed in reaching the central position 
we may have fatigued the reader on the road or produced 
sensations which prevent the unbiassed contemplation of 
the whole view when it is presented. With us the whole 
IS only the sum of its many parts, whereas with the artist 
the parts are merely fractions of a united whole In 




Some peri- 
ods of his- 
tor>- take 
their name 
from some 
great event 


No central 
event in o\ir 

treating of the thought of the century, even within the 
narrow limits which have been prescribed, I am met with 
similar difficulties. In the large circumference of the 
domain of thought I have to choose a starting-point and 
to construct a road which may lead to the central position, 
hoping there to gain a comprehensive view of the whole. 
Some periods of history are characterised by one great 
and central movement which absorbs all active forces 
and all intellectual and imaginative power, making 
them either subservient to one end and purpose, and 
helpful in the elaboration of one idea; or else forcing 
them into opposition, where they testify equally to the 
importance of this central movement. Such periods 
were, for instance, the long centuries of Jewish history, 
the early age of the Christian Church, the period of the 
culmination of Papal power, the Eeformation, the French 
Eevolution. In studying the thought of such ages, we 
are not at a loss where to find the leading idea, — we 
easily fix the centre of the vortex which draws into its 
motion all the existing forces, all genius and all talent. 
In an age like that of the Eeformation we can speak of 
the Politics of the Eeformation, the Eeligion of the Eefor- 
mation, the Philosophy, Literature, and Art of the Eefor- 
mation, and we are pretty sure to embrace under these 
various heads an account of all the mental progress and 
to trace all the thought of that age, be it friendly or anta- 
gonistic. It is evident that no such central event, no such 
all-absorbing vortex of motion, exists in the period which 
we have lived through. The uniting bond, if it exists, lies 
much deeper ; the problem we have been engaged in solv- 
ing, the prize we are fighting for, does not present itself on 


the surface ; it is not explicitly stated, it must be implied 
rather than defined. The great object of our life and 
labour has not been clear to us, as it seemed clear to those 
who lived during the Eeformation or the Eevolution, other- 
wise we should not have philosophies of the Unconscious 
and of the Unknowable, and the century would not end 
m asking, Is life worth living ? 

Then, again, we find in history long periods of quiet 
development, where men's minds seemingly run very much 
in the same direction, exhibiting a general tendency of 
Ideas the spreading of a defined habit of thought and of 
simple methods, the application of a few principles : such 
a period was that preceding the French Eevolution the 
greater part of the eighteenth century. It has therefore 
been easy to characterise that century: it has been 
termed the philosophical century, the century of the 
Aufklamng, the century of Voltaire.^ No such one 

political and literary work of the 
last century. The first draft of it 
appeared in 1824, after Schlosser 
had passed two years in Paris, where 
no doubt he must have come under 
the influence of Villemain. The 
work itself began to appear in 1826 
and was finished in 1848. It is 
considered to be Schlosser's greatest 
work, and had a large circulation. 
Ihe connection of political and 
literary history was studied by 
Gervmus, who with Hiiusser is 
usually counted as a pupil of 
I Schlosser. But the great work 
j which Villemain had begun and 
Schlosser taken up was adequately 
j carried out by Hettner, who in 
his ' Literaturgeschichte des acht- 
zehnten Jahrhunderts ' conceived 
the whole intellectual movement of 
that age as a battle for enlighten- 
ment {Kampfder A ufkldrwng). The 

The first who reviewed the 
literature of the eighteenth century 
from an international point of view 
was Villemain, who as early as 1820 
was engaged in lecturing at the 
borbonne before the aUe of the 
rising literary generation of France 
on the literature of the eighteenth 
century, taking France as the centre 
and showing the influence of foreign 
literature, especially English, as like- 
wise the reaction of French ideas 
abroad. He was too early to recog- 
nise the true meaning of the new 
spirit which had then already gone 
forth from Germany. In this respect 
his • Cours de Litterature francaise,' 
published in 1828 and republished in 
1864, remains incomplete. Schlosser 
next attempted to present in his 
Geschichte des achtzehnten Jahr- 
hunderts,' after the manner of 
l^ibbon, a picture of the combined 






Is history 
of thought 
history of 

^ ^•..A fr^ mir ncrp no one name can be 

term can be applied to our age, no ui 

found which carries with it the recognition of all the 
many interests which surround us. 

It has been suggested by some that the history o 
octhought thought is equivalent to the history ^^ PJ^^^^^^^^^^^^^^ 
"^^^ the different philosophical systems and theories exhibit 
in the abstract the course which ideas have taken m an 
ace^ A history of thought in the nineteenth century 
w^uld thus mean a history of nineteenth century philo- 
sophy. There have indeed been plenty of philosoph^^^^^ 
and systems during our period, but m spi^ of their 
.reat number and variety-ranging from the extreme 
Idealism of Fichte to the equally extreme materialism 
of Blichner^— we feel that they do not cover the whole 
area of thought. The period in -r century which m 
England was most barren in philosophy, the first forty 
years, produced an entirely new literature and a nove 
conception of art, both containing new sources of mental 
life, though they have hardly yet found expression m any 
philosophical system. Equally barren in speculation was 
France during the Eestoration ; yet there, too, was a 

latter part of his work deals with I 
the reaction against Aufklarung 
and "Rationalism" as it began in 
England, and was represented on 
the Continent by Rousseau and 
the earlier ideals of the French 
Revolution. Through Rousseau and 
the Revolution the growing in- 
fluence of the new spirit of English 
literature was overpowered and lost 
for the Continent. And, as we have 
to regret in ViUemain his neglect 
of the new life of Germany, so we 
have to deplore that Hettner fol- 
lowed the developments of Rational- 
ism aud Aufklarung only in the 

form they assumed in Germany, 
neglecting to notice the contem- 
porary growth of the new life m 
English Literature and Art, to 
which, in fact, no German historian 
has as vet done justice. 

1 See especially Hegel's Lectures 
on the History of Philosophy m his 
collected works, vol. xiii. p. 68 «^'/- 
(Complete edition, Berlin, 1832.) 

2 The principal publications of 
this school are Vogt, ' Physiologische 
Briefe,' 1845-47 ; Moleschott, Der 
KreislaufdesLeben8,'1852; Buch- 
ner, ' Kraft und Stoff,' 1855. 



brilliant era of literature, and the whole of Europe was 
illuminated by the light of science which emanated from 
Paris during the first third of this century. History of 
philosophy has little to say about Goethe, though his woSYn- 

» to volvesthe 

work embodies for us probably the deepest thought of f^^^^^^ ^f 
modern times. Again, the only great and novel system ^^^ century. 
of philosophy which France has produced during this 
century is that of Comte, but it has had only small 
influence in its own country ; and who would say that 
it reflects French thought of the period as Voltaire 
and Montesquieu reflected the thought of the last 
century ? Hegel himself, who was intent upon tracing 
the working of the human mind in the systems of 
philosophy, declared that philosophy is the latest fruit 
of civilisation, — that the special idea which governs any 
period is already dying out when it appears in a system.^ 

^ The principal passage expound- 
ing this idea of Hegel's is to be 
found in the introduction to the 
course of lectures which he delivered 
at Berlin repeatedly during the years 
1816 to 1830. See his collected 
works, vol. xiii. p. 66 : " Philosophy 
makes its appearance at the time 
when the mind of a nation has 
worked itself out of the indifferent 
dulness of the early life of nature, 
as well as out of the period of pas- 
sionate interest ; inasmuch as the 
direction towards detail has spent 
itself, the mind transcends its 
natural form — it passes on from 
practical morals, from the force of 
real life to reflection and compre- 
hension. The consequence is, that 
it attacks this actual form of exist- 
ence, these morals, this faith, and 
disturbs them ; and with this comes 
the period of decay. The further 
stage is, that thought tries to collect 
itself. One may say, that where a 

people has come out of its concrete 
forms of life, where distinction and 
separation of classes has set in, 
where the nation approaches its 
fall, where a rupture has taken 
place between the inner desires and 
the external reality, where the rul- 
ing form of religion, &c., &c., does 
not satisfy, where the mind shows 
indifference towards its living exist- 
ence or lingers discontestedly in it, 
where moral life is in dissolution — 
then only does one philosophise. 
The soul takes refuge in the realms 
of thought, and in opposition to tlie 
real world it creates a world of ideas. 
Philosophy is then the reparation of 
the mischief which thought has be- 
gun. Philosophy begins with the 
decline of a real world : when she 
appears with her abstractions, paint- 
ing grey in grey, then the freshness 
of youth and life is already gone ; 
and her reconciliation is not one in 
reality, but in an ideal world." 





6. This means that philosophy is retrospective : it sums up, 
retrospec- it ciiticises, it does not prefigure the future. The correct- 

ness of this proposition may be doubted. We shall have 
to deal with it in another place. At present it reminds 
us that thought, in the sense in which we take it, cannot 
be identified with philosophy, and hence a history of 
philosophy in the nineteenth century is not identical 
with a history of its thought. There is indeed a sense 
in which the word philosophy is sometimes used, when 
it approaches more nearly to the meaning of the word 
thought, as we intend to use it. Whewell has in this 
sense written the philosophy of the inductive sciences, 
meaning to trace in that work the processes of thought 
which are consciously or unconsciously employed in 
scientific research and reasoning, and which lead to 
7. progress in science. Something similar might be at- 

"WTien does . 

thought tempted m regard to art, commerce, politics, government, 
sophy? religion, and literature generally. In every case philo- 
sophy would simply mean the peculiar way of thinking 
and reasoning which is adopted in these various branches 
of practical or intellectual life. This is, however, not the 
sense in which the word philosophy is generally used. 
It generally denotes something more than a statement of 
method or a rationale of ideas and reflections ; it denotes 
a definite theory, an explanation of a larger or smaller 
circle of phenomena. As such it certainly forms a part 
of the thought of the century, probably the most in- 
teresting and fascinating part; but it is also that 
which is most liable to change, most subject to discus- 
sion ; whereas the other more hidden thoughts and reason- 
ings form, as it were, the ground upon which all the 

intellectual, artistic, and practical achievements of the age 

It would thus appear as if an account of the thought of s 

investigations. In the iirst place, we should regard thought ^" SZ 
merely as a means to an end, as the method adopted to -"" '^ 
attain a certain purpose, be it practical or theoretical It 
wou d mean the peculiar kind of reasoning which has been 
employed m the search for knowledge ^r in its useful 
application As all reasoning starts from certain assump- 
tions, called premisses, or principles, or axioms, and pro- 
gresses from these by certain methods, this portion of our 
task would divide itself again into a statement of the 
principles which underlie, and an account of the methods 

But thought does not exist merely for the sake of in- 
creasing our knowledge of things and of applying this to 
practical purposes. Occupied in this way meref, it re- 
mams fragmentary, incomplete, and not infrequently it 

purely to detailed research or to practical work are again 
and again compelled to take a wider and deeper view of 
things than their special occupation affords. One may 

useless f *'\"^*°'^^ ^^^^ ^« - "-g daily become • 
useless for certain practical purposes he has in view and 

half h s hfetime he has applied with unquestioning faith 
m their validity and usefulness. Another may hafe m t 

search, that he wishes to apply it to subjects which were 
previously handled in a different manner, or elevat IZ 




the dignity of a general rule of thought. A third may, 
accidentally, be interested in two or more pursuits which 
are seemingly unconnected, but which — being brought 
side by side in his mind — he feels the wish to unite 
and harmonise. A fourth may, at a certain time of life, 
grow tired of the drudgery of petty pursuits which never 
carry him beyond a very limited sphere of interests : he 
is tempted to look beyond this narrow range, and gain 
some wider view of other pursuits and interests. Allowing 
that ignorance or indifference prevents even the majority 
of those whose powers are not exhausted in the struggle 
for mere existence from looking much beyond their nar- 
row circle, allowing also that many of us live — like chil- 
dren — in a blessed trust that the great and important 
interests of mankind are under higher and better guidance 
than we can understand or control, there still remain a 
considerable number of persons who are always on the 
look-out for something higher, wider, and better, who are 
driven by an undying thirst after real wisdom, or by an 
inherent restlessness of disposition to inquire into the 
deepest foundations and the ultimate ends of the world 
and life. Language has coined a word which denotes the 
whole of these occupations and endeavours, how various 
so ever they may be, and for whatsoever purpose they may 
be undertaken. It calls them speculations. The word 
also indicates the venturesome and risky nature of these 
undertakings. They have existed in all ages and countries 
and languages wherever literature has existed, and have 
been carried on by the powers of reason or imagination, 
in prose, verse, or symbol, sometimes in defined and clear 
terms, more often in mystic allegory. Philosophy may be 


said to have grown out of these vague and scattered 
begmmngs by the attempt to conduct them accord t 

sistent whole. Philosophy may thus be defined as specula- . 
^on earned on according to some clear method, alat &- 
mg at systematic umty.^ Both science and philosoBhv 
-ay be called methodical thought, but the .or!^yZl 

imZ: T ' '^ ^'^ '^^'^^ ^^^ -- ^^— ^ ^- 

ieotlZlrrZ^ '' ' """' "^'^'^ ^' ^- ob- 
ject. In the first we have to consider thought merely as c 

a means to an end ; in the second we have toLside" ^ a 

te^tTnlt """' ''' ^"" ^^^^^^' ''' ^^-' i^« -Mity, of 
certainty, completeness, and unity. The whole If th. 

Lotze 8 definition (see * Grundziige 

Ihe commoii culture of life and 
^e separate scU^es contain a num 
oer of suppositions the origin of 
which IS obscure to us, because ?hey 

Tf ml" *^'^"^^ *^^ comparison 
thev h3 rP.T'°'^'» ^^ because 
means nf ^''^^^^^^^ conscious by 
means of auch experiences, have 
then received definite names and bl! 
come habitual without having been 

th.p . \^^! u^^"^°' *^« «eosc. and 
the extent of their validity. In this 

way science and life make use of the 

and r "' T'' '°^ '^'^'^ ^' ^'^r 
and force, of means and end, oi free- 
dom and necessity, of maiter ^Zd 
VOL. I. 

rntnd, and they frequently entangle 
themselves, owing to the above-n^en! 
tioned defect, in contradictions In- 
asmuch as they are unable to fix the 
limits of validity of these to some 
extent contradictory assumptions, 
^ow we may formally define 


It J A ° ^^^eavour to import 
unity and connectedness into the 
scattered directions of cultured 
thought, to follow each of these 

fn\T rL"'' '"^ assumptions and 
ihem^l ?°^T^°«««» to combine 
them all together, to remove their 
contradictions, and to form out of 
them a comprehensive view of the 
worid mainly, however, to subject 
those Ideas which science and itfe 
regard as pHnciples to a spec al 

W °^/ i° ?-der^ determinf hi 
limits of their validity. " 


science nor 
the whole 
meaning of 
the word 


also hidden 
in the liter- 
ature and 
art of the 


term Philosophy ; and as the first part wUl deal wixh 
the scientific, so will the second deal with the philo 
sophical thought of our century. 

Science has gradually risen out of the mass of accu 
Jated hut Lccurate and disorderly knowledge by 
the desire of making it accurate, orderly, and use^^uL 
Philosophy has similarly emerged from the great world 
of specVative thought by the desire of carrying J 
on methodically and for a defined end and purpose 
Nevertheless neither the one nor the other nor bo h 
together, really exhaust the whole meamng of the word 
« Thought"; neither science nor philosophy covers he 
whole Wo; of thought. Both are comprised under the 
term methodical thought; but there remams the great 
Ly of immethodical, undefined thought. This is buned 
^general literature, in poetry, fiction, and art, it shows 
its practical influence in the artistic, moral, and religious 
life of our age. It is a reflection of the knowledge of 
cience or the light of philosophy, but, like all reflect d 
licht it not only follows, it also precedes the real and full 
i:ht': it is not only the dusk that comes after it is also 
the dawn that comes before the day, it is the twilight 
of thought. In it lie hidden the germs of future thought, 
the undeveloped beginnings of art, philosophy, and science 
yet unknown and undreamt of ; it encloses -d -rrou^^^ 
L innermost recesses of the mind, where all thought had 
its origin, and whence it ever and again draws fresh life 
and inspiration. 



1 This is originally a Leibnizian 

idea. It is laid down in the doctrine 

' of the petites perceptions, as given 

in the introduction to the Nou- 
veaux Essais,' and referred to in 
many passages of Leibniz s various 

No account of the thought of our century would be 
complete or satisfactory which took no notice of this great 
volume of immethodical and unsystematic thought which 
lies buried in the general literature and in the art of 
the age. Both have shown a vitality, originality, and 
versatility which exceed that of any except the few 
favoured periods — those of Athens under Pericles, Italy 
during the Renaissance, and England under Elizabeth. 
In one of the arts, in music, our age has, according to the 
opinion of many competent judges, exceeded in originality 
and certainly in productiveness all former ages. In 
poetry Goethe and Wordsworth have raised our tastes u. 
and demands to a higher level, in fiction France and wordswo^h 

-c 1 J T_ 1 raised our 

hngisLna have almost created a new branch of literature, I **'^^- 
whilst the peculiar features of modern English landscape- 
painting were unknown to previous centuries. All this, 
though produced under no scientific or philosophical rule 

writings. See 'Nouv. Ess.,' Pre- 
face, Leibniz, Philosophische Werke, 
ed. Gerhardt, vol. v. p. 48 : — 

"Ces petites perceptions son t done 
de plus grande efficacepar leur suites 
qu'on ne pense. Ce sont elles qui 
forment ce je ne S9ay quoy, ces 
gouts, ces images des qualit^s des 
sens, claires dans I'assemblage, mais 
confuses dans les parties, ces im- 
pressions que des corps environnans 
font sur nous, qui enveloppent 
I'infini, cette liaison que chaque 
estre a avec tout le reste de I'uni- 
vers. On pent meme dire qu'eu 
consequence de ces petites percep- 
tions le present est gros de I'avenir 
et chargd du passe, que tout est 
conspirant (trvixirvoia ir<£i»Ta, comme 
disoit Hippocrate) et que dans la 
moindre des substances, des yeux 
aussi per^ans que ceux de Dieu 

pourraient lire toute la suite des 
choses de I'univers. 

" Qua) sint, quae f uerint, quae 
mox futura trahantur. . . . C'est 
aussi par les perceptions insensibles 
que s'explique cette admirable har- 
monic preestablie de I'dme et du 
corps, et meme de toutes les Mon- 
ades ou substances simples, qui sup- 
plee a I'influence insoiitenable des 
uns sur les autres, et qui au juge- 
ment de I'auteur du plus beau des 
Dictionnaires exalte la grandeur 
des perfections divines au delh. de 
ce qu'on eu jamais con^u." 

The importance of this idea of 
Leibniz has been dwelt on at length 
by Kuno Fischer in his ' Geschichte 
der neueren Philosophic,' where he 
also traces its influence in the 
development of philosophy and 
literature in Germany after Leibniz. 





and very frequently outside of any school, points to novel 
modes of mental conception, to a fund of ideas yet im- 
developed or only partially developed into clear thought. 
The whole of this productiveness indicates a vast amount 
of mental work which, though not yet absorbed by science 
or philosophy, belongs nevertheless, according to our 
original conception, to the world of thought. The mean- 
ing of it may be enigmatical, and the clear expression 
which it will some day produce in philosophical and 
scientific reasoning may be far distant and unintelligible 
15. to us now. Still there it is, this great body of undefined 
cai thougiit.' thought, this volume of diffused light, the focus and 
centre of which is still hidden from us. We feel that in 
discussing the thought of the century we cannot pass it 
by or neglect it. 

It is difficult to find any one term under which we 
could comprise this great body of unmethodical, scattered, 
and fragmentary thought, — any one word, similar to 
science and philosophy, in which we could sum up and 
characterise its general meaning and tendency. So far 
we have only stated what it is not, what to a large extent 
it perhaps never will be — viz., methodical. And yet we 
feel that it contains that kind and portion of thought 
which touches our deepest interests, our most intimate 
concerns, our noblest aspirations. Science becomes more 
and more a mere calculation, une qitestion d'analyse, an 
occupation for the laboratory, the workshop, the manu- 
factory, and the market ; philosophy savours at its best 
too much of the school and lecture-room, runs too much 
into systems and categories, it fatigues us with definitions 

and abstractions. But neither calculation and measure- . 
ment nor dehmtion and abstraction, suffice to exhaust «e 
what IS to us, m the quiet and serious moments of life of ^^"^ 
the deepest, our religion. I use the w^rd """"" 
here m its original sense, and I propose to sum up in the 
term r^hgxous thought the whole of the thought contained 
n that large volume of literature which does not submit 
to scientific and philosophical treatment, but which never- 
theless forms so important an outcome of the mental life 
or the century. 

There are other words more or less current in modem 
literature that may serve to throw some light on the 
distinction that I am here drawing for the purpose of 
affordmg a preliminary view of the course to L pur- 
sued in the following treatise. 

Science is said to be exact, positive, and objective, and „ 
It IS opposed to such other thought as is inexact, vague, e-^pi^, 
and subjective Science is said to convey its results or^'5ti£ 
Ideas in defined, direct, and general terms, whereas there 
18 a large department of literature and thought which 
moves in undefined, symbolical, and indirect expressions. 
So ence professes to rest on clear and precise knowledge, 
and IS thus opposed to such other realms of thouc^ht as 
rest on opinion, belief, and faith. It may be well t^ note 
here that these different terms refer either to the method 
of treatment or to the matter which is under treatment. 

metT.' r. ''f "" "^ '^^^ ^ ^^"^ -d -disputed 
me hod. Other branches of thought either borrow their 
methods from science, or they have fluctuating, not gener- 
ally recognised methods, or they refuse to submit to method 





Some in* 
terests or 
objects of 
thought are 
personal or 

on these 

altogether. But so far as the matter under treatment is 
concerned, a clearer division is possible. Science deals 
with all such things or objects of thought as are common 
to a great many persons and — under certain circumstances 
are accessible to everybody : it thus claims that its ob- 
servations and reasonings can be checked and submitted to 
repeated examination and verification ; so that a large por- 
tion of them can always be regarded as settled and agreed 
upon, and can be taken for granted and used as a secure 
foundation by those persons who are themselves unable or 
unwilling to go through the process of verification. But 
there are a great many things and interests which centre 
in the individual mind of each person— which are, in fact, 
personal, individual, or subjective. They are to all of us 
just as important as the others. They form the real sub- 
ject-matter of all that thought which is separated from 
science, and in its very nature and aspect opposed to it. 
In this great province of thought one pei^on cannot do 
the work for many in the same way as is possible in 
science. Proof is almost impossible, and agreement refers 
always only to a certain number of persons. Doctrines or 
theories in this region of thought cannot be accepted and 
taken for granted as they are in science, but every person 
must go over the same ground for himself before he has 
any right to accept or make use of what is given to him. j 
The real and true character of all this thought is that it 
is individual and personal, whereas all scientific thought 
whatever its origin may be — must be general and im- 
personal. At the extreme end of thought in one direction 
are placed the mathematical sciences, at the extreme end 
in the other lies religion. Disagreement in the former is 

almost as unknown ^ as agreement in the latter. There 
we have an almost universal unity of thought ; here unity 
of thought probably never existed ; it is unknown. Popu- 
larly we can say that at the one extreme lie knowledge 
and certainty, at the other faith and belief. There is, 
however, a very large extent of ground between these two' 
extremes. This is covered byall such intermediate thought 
as rests partly on knowledge, partly on faith, where cer- 
tainty is largely mingled with belief. This large inter- 20 
mediate region, where changes and fluctuations are fre- SeS-^ 
quent and rapid, is the proper home of philosophy, which ^^^^^^ 
occupies itself with the grounds of certainty and belief, ^^'Si^. 
the origin of knowledge and faith, and the relations in 
which both stand to each other. Were all our thoughts 
either purely mathematical — i.e., referring to number, 
measurement, and calculation, or purely religious— i.e.,' 
referring to our individual concerns and personal convic-' 
tions, — the need of a continued compromise or mediation 
would be unnecessary, the question as to the grounds of 
certainty or belief would never arise. But no sooner 
do we wish either to apply our strict mathematical no- 
tions and processes, or to bring our personal convictions 
into practical use, than the two kinds of thought come 
into contact, not to say into conflict, and there is need 
of some theory according to which this contact may be 
regulated, this conflict settled. And as the occasions for 
such contact change with the demands of practical life, or 

It may be doubted whether this 
is quite correct, looking at the con- 
troversies which have been connec- 
ted with many mathematical theo- 
ries—such as the theory of parallel 
lines, the meaning of infinitesimals, 

the correct measure of force. 
These controversies, however, re- 
ferred really to applied, not to pure 
mathematics, and were settled by 
introducing correcter and more 
stringent definitions. 






tion of 
thought : 
cal, indi- 

the progress of applied science, these theories must them- 
selves change and develop. Now it may be generally 
stated that it is the task of philosophy to take note of 
these different ways by which the strict methods of science 
are applied and made useful, or by which personal and 
individual convictions are brought to bear upon practical 
questions which are not only of personal but of general in- 
terest and importance. It does not follow that philosophy 
must necessarily construct a complete system ; but it is a 
natural and frequent occurrence that the occupation with 
a great number of detached theories or aspects of thought 
generates the desire to bring them into harmony and to 
unite them in a connected whole. Thus the enterprise 
which was originally purely critical and preparatory, and 
undertaken merely as a means to an end, may lead to the 
formation of a general and all-embracing view of things 
— i.e., to a philosophical system. 

From whichever side we approach the matter, we are 
thus always led to a threefold consideration of thought, 
as scientific, as individual, and as philosophical. An at- 
tempt in which any of these three aspects were neglected 
could have no value in an account of the thought of our 
age. There have indeed been schools of thought which 
identified science with philosophy, or which maintained 
that no independence belonged to religious, personal, or 
individual thought, inasmuch as this was merely of a 
derived character. Though such theories may have ex- 
erted considerable influence, they have as a whole failed,^ 

^ This can be said of Hegelian- 
ism as well as of Comtism. In the 
former it was a favourite doctrine 
that philosophy was the higher 
wisdom compared with religion and 

art. See Hegel, * Geschichte der 
Philosophie ' (Werke, vol. xv. p. 
684) : " The highest aim and inter- 
est of philosophy is to reconcile 
thought, the idea, with reality. 

and we find ourselves at the end of a long and critical 
period unable to say that any one of the three realms 
otjhought has gained an undisputed victory over the ' 
others. Science is more than ever that kind of thought 
which gives knowledge and certainty. Eeligion is still 
the generally recognised abode for those convictions 
vvhich refer to our deepest personal interests. And more 
than ever do we feel the need of a reconciliation of both ., 
in some theory of life which is neither purely scientific nor ™» 
purely individualistic ; and this means that philosophy is -'e- -<." 
as much needed as ever. Our centuiy has witnessed ar"'"- 
great development of scientific thought, a great revival in 
rehgious interest, religious feeling, and religious activity ' 
and It IS probably richer than any preceding age in 
philosophical theories and systems.! 

I must repeat here what I said above, that it is a 
misfortune that in dealing with a complicated subject 
we are obliged to divide it,-that we are forced to ive 
preference to some one aspect, and to choose a spedal 

Philosophy is the veritable theo- 
dicy, compared with art and religion 
and their sentiments— this recon- 
ciliation of the mind, indeed of that 
mmd which has grasped itself in the 
freedom and wealth of its reality. 
It IS easy otherwise to find satisfac- 
tion m subordinate regions of intui- 
tion and feeling," &c, &c. Al- 
though it 18 an exaggeration to say 
that Hegel desired to absorb or 
evaporate religious belief in philo- 
sophical knowledge, as his lengthy 
explanation (Introduction to the 
Histoiy of Philosophy,' Works, vol. 
xiii. p. /7 sqq.) sufficiently proves, 
there is no doubt that the senti- 
ment expressed in the above pas- I 
sage indicates that philosophy was 
commg to the rescue of true reli- 

gious belief, which threatened to be 
lost m the rationalistic and mystical 
schools of the day. And this had 
tne further consequence that a 
scientific occupation with or inter- 
est m religious subjects— be it meta- 
physical or historical— took the 
i Pl^e of a purely religious interest, 
j and that many eminent German 
theolopans became either pure 
metaphysicians or merely critics, 
the practical side being lost sight of 
It IS probably just as incorrect 
to accuse Comte of an intention 
to destroy true religion because he 
preached the well-known doctrine 
ot the three stages of human 
thought-the theological, the meta- 
physical, and the scientific or posi- 
tive. * 





point from which to set out. In dealing with the 
thought of our age, I have been obliged to divide what 
is in reality connected and coherent ; and I am further 
forced, in examining more closely its different aspects, 
to select one as the most prominent with which to make 
a beginning. In reality such a preference does not exist 
in my plan. I recognise all the aspects of thought as 
equally important, and I feel that I might begin with 
any one of the three, and that I should in due course be 
js. led on to a consideration of the other two. They are in 
S^t ^e their actual historical appearance in the course of our period 
^^f 80 interwoven that they cannot practically be separated. 
And it is indeed not difficult to assume various positions 
in contemplating the whole subject from which either one 
or the other of the three forms of nineteenth-century 
thought assumes as it were the ascendancy. Thus it 
would be undeniable that from a German point of view 
the great movement of ideas centred in the first third of 
the century in what I have called philosophy. The 
number of systems which succeeded each other was 
astonishing, the influence they had on literature, science, 
dnd practical life was without precedent, the enthusi- 
asm with which students from all parts gathered in the 
lecture-rooms of the great metaphysicians was quite 
extraordinary, and probably equalled only in the schools 
of Athens in antiquity, or in the lecture-room of Abelard 
in the middle ages. From this point of view an account 
of this great movement— how it grew, flourished, and 
died away— would no doubt afford a suitable introduc- 
tion to the history of thought in our century. If after 
this we were to turn to France and try to fix upon the 

most striking intellectual feature of the century, it would 
be the equally great and remarkable array of scientific 
names of the first magnitude. In France during the 
early part of the century the foundation of nearly all the 
modern sciences was laid ; many of them were brought 
under the rule of a strict mathematical treatment. It 
was there that scientific subjects were made so popular, 
and clothed with a garment of such elegant diction, that 
they have since that time greatly entered into general 
consciousness, and have promoted in literature and art 
an independent school — the naturalistic. Compared 
with this mathematical and naturalistic spirit, philo- 
sophy proper has found but a meagre development and 
culture in France: the constructive tendency of ideal- 
ism has found nourishment for the most part only in 
leanings to the older systems of Descartes, Plato, and 
Aristotle, or to the foreign ones of Hegel and other 
German metaphysicians. Compared with Germany in 
philosophy, and with France in science, England during 
the early part of the century appears remarkably unpro- 
ductive. English science and English philosophy had 
flourished in the seventeenth and eighteenth centuries, 
and leavened the whole of European thought, but in the 
beginning of our period we find neither represented by 
any great schools. The great discoveries in science be- 
longed to individual names, who frequently stood iso- 
lated ; the organisation and protection which science could 
boast of in France was then unknown in England ; into 
popular thought it hardly entered as an element at all. 
Metaphysics had not recovered from the blow which 
David Hume had struck, and speculation was confined 

centred in 
science dur- 
ing the first 
part of the 

State of 
in the early 
part of the 
century in 




' Faust ' re- 
tive of the 
thought of 
the century. 



A period 
not of re- 
pose but of 

almost entirely to the novel field of social and economic 
problems. But against this there was a young growth 
of ideas springing up in the poetic literature of the 
nation. It is the freshness of individual thought as 
clothed in the poetic language of Shelley and Words- 
worth, maturing and deepening in the works of Tennyson 
and Browning, which strikes us as the most original phase 
of English thought in this century, whether we compare 
it with Continental thought of the same period, or with 
English thought of the previous age. 

And lastly, we might be tempted to make the great 
work of the greatest mind of the early part of our period, 
Goethe's ' Faust,' the centre and beginning of our survey, 
singling it out as a comprehensive embodiment, as the 
classical expression of nineteenth - century doubts and 
aspirations, leading us — if we try to understand it — 
now into the bewildering labyrinth of philosophy, now 
into the cheerful expanse of natural science, and again 
into the hidden depths of individual life, of religious 
faith with its mysteries of sin and redemption. 

But from whatsoever point we may start on our journey, 
from whatsoever easily reached eminence we may cast a 
first eager glance across the wide country which we wish 
to explore, there is one feature which impresses itself 
alike upon our minds from the very beginning. It is not 
a country of repose and restfulness, of healthy industry 
and quiet work, of gradual development, of ripening 
crops, of sowing or ingathering ; it does not present the 
aspect of a happy division of labour, of successful co- 
operation, of peaceful regulation of employment. It looks 
more like a land which has lately been disturbed by 



great elemental forces, heaved up hy an earthquake or 
visited by a destructive storm. We see some persons em- 
ployed in fining up great breaches and recently made rents 
others trying to lay new foundations ; others again are 
fighting for their possession or trying to divide a disputed 
territory; even the peaceful workers are called out to help 
in the battle, or disturbed by the complaints of their 
neighbours, on whose ground they are trespassing un- 
awares, whose foundations they are unconsciously under- 
mining. If we inquire into the cause of this unrest and 
anxiety, which seems to be a feature common to nearly 
all the phases of nineteenth-century thought, we must 
look back to the age which immediately preceded it. It 
IS the storm of the revolution which passed over Europe 
and shook to the foundation all political and social in- 
stitutions, that has likewise affected our ideas and thoughts 
in every direction. The period we refer to has thus not 
incorrectly been termed a century of revolution. If in 
spite of this I decline to consider nineteenth -century 
thought as essentially revolutionary, it is because the 
work of destruction belongs in its earlier and more 
drastic episodes to the preceding age. The beginning 
of our period witnesses everywhere the desire to recon" 
struct, either by laying new foundations or by reverting 
to older forms of thought and life which it tries to 
support by new arguments or to enliven by a fresh in- 
terest and meaning. We may say that the thought of 
the century in its practical bearings is partly radical 
partly reactionary,— meaning by the former all those 
constructive attempts which try to go to the root of 
thmgs and to build up on newly prepared ground ■ by 


Cause of it 
seen in the 
century of 
preceding it 

not revolu- 

Thought of 
this century 
partly radi- 
cal, partly 




The thought 
of Bums, 
worth, and 
disturbed by 
the Byronic 

spirit in 
writings of 

the latter all those endeavours which, clinging to his- 
torical institutions and beliefs, aim at finding the truth 
and value which are in them, and the peculiar importance 
which they may have for the present day. The work of 
destruction is indeed still going on ; in the midst of this 
constructive or reconstructive work we still witness the 
workings of the revolutionary spirit. The healthy new 
life which Burns, Wordsworth, and Coleridge infused into 
English poetry at the beginning of our period was dis- 
turbed in its quiet growth by the revolutionary spirit of 
the Byronic school. The new thought, which grew up in 
Kant's philosophy and the idealistic school, degenerated in 
its further development into a shallow materialism and 
a hopeless scepticism. But none of these destructive in- 
fluences, however passingly interesting they may have 
been, seem to have struck out any new line of thought. 
Whoever wishes to study the arguments by which social 
order was subverted and cherished beliefs destroyed will 
find them brilliantly and consistently expounded in the 
writers of the eighteenth century, from which many 
nihilists of our age have drawn their inspiration. This 
is not the task which I have in view. It has been per- 
formed in our time by many writers of great eminence. 
Nor do I intend to describe the courses which governments 
and politicians have taken in dealing with the legitimate 
demands of the people, such as a hundred years ago found 
a memorable expression in the American Declaration of 
Independence, and an exaggerated one in the cry of the 
French Kevolution. Only to a small extent has the ideal 
of that great movement, as it lives in the mind of many 
a democratic leader, been realised in our century. In 


most European countries the work of national unification 
and consolidation, and the struggle for political indepen- 
dence, have retarded internal reforms ; nor have theorists 
been able to agree in what form of social organisation 
hberty and equality could consistently live side by side 
Their teaching must indeed command special attention 33 
as one of the many forms of the philosophic thought of f^/rS 
the age; but a wide gap separates theory from practical ^•'"'''' 
politics, which have been largely occupied with wars and 
diplomatic feats, or, when they really dealt with social prob- 
lems, have had to be content with awkward compromises 
between prejudices and institutions of bygone ages on the 
one side, and legitimate demands for freedom on the other 
Though much practical thought and much labour have 
been spent in achieving even these moderate results, I feel 
that they really fall outside of my programme. Wherever 
either science or philosophy steps out of the quiet regions 
of the study, the lecture-room, and the laboratory or 
wherever religious faith leaves the secret recesses of 'the 
believing soul to solve the problems of life or to perform 
the work of the day, the line is crossed which I have felt 
obliged to draw around the following sketch. Not that I 
do not recognise this borderland, where the spirit subdues 
matter, where thought becomes useful, where the idea 
attains reality, this field of strife and endeavour, of patient 
toil and slow victory, as by far the most important subject 
of history, and as that in which our age has probably 'ex- 
celled every earlier period. But an account of this side of 
nmeteenth-century life could ill afford to limit its view to 
the three principal countries of the Old World. For where 
are discovery and invention at this moment more at home 


This is not 
a history of 
or of practi- 
cal politics. 


Thought to 
be consid* 
ered in its 
tive, not 
in its de- 


than in America; where have political theories, the original 
riahts of man, the ideas of liberty, equality, and brother- 
hood been more widely put to the test ; where have reh- 
gious beliefs entered into closer contact with the work of 
the day ; or where in our age has the simple rule of early 
Christianity been more successfully put into practice ? 
An account of the application of thought taken merely 
from our European experience, where half our endeavour 
must always be spent in clearing away obstacles, in 
removing the debris of antiquated institutions, m over- 
coming prejudice, or battling with evils which have grown 
to uncontroUable magnitude, would give us but a poor 
notion of the influence of thought over material circum- 
stances, and a very exaggerated one of the inertia of the 
mechanism of older societies. With the work of the in- 
ventor the practical statesman, or the lawgiver, I have thus 
nothing to do at present ; only in cases where practical 
problems have immediately reacted upon scientific research, 
or where social questions have given rise to special theo- 
ries shall we be compelled to cast a glance outside of the 
inner world of thought into which I invite my readers to 


This inner world has, indeed, not been all rest and peace 
and quiet development. No age has been so rich in rival 
theories, so subversive of old ideas, so destructive of prin- 
ciples which stood firm for many ages', as ours. It is not 
my intention to emphasise this critical or radical tendency 
more than is necessary. True to the original view which I 
have already expressed, I intend to look upon thought as 
a constructive, not a destructive agency ; on the world of 
ideas as a positive axjquisition, not as a mere counterpart 



or shadow of material existence. Though demanding for 
its growth an outer stimulus, and unable to proceed very 
far without external correctives, I nevertheless maintain 
that the human mind in its individual and collective life 
encloses an independent source of reality which contact 
with outer things and thought in all its various forms 
has to reveal, to preserve, and to develop. To what 
extent this has been done in our century is the question 
I propose to answer. With this object in view I shall 
try to gather my observations and my narrative around 
the prominent and novel constructive ideas which have 
sprung up in the course of the century, not omitting 
the great development which the purely formal side of 
thought, the method of research, has undergone. Such 
constructive ideas are those of energy, its conservation 
and dissipation ; the doctrine of averages, statistics, and 
probabilities ; Darwin's and Spencer's ideas of evolution 36. 
in science and philosophy ; the doctrines of individualism speTJeA, 
and personality, and Lotze's peculiar view of the world constroctlve 
of " values " or " worths." Around these centres of thought 
cluster the many critical oppositions, the great contro- 
versies of radical or conservative opponents. As regards 
these, I shall welcome all radicalism which lays bare the 37. * 
roots of our ideas, which delves deep into the ground Jo'^jL^di. 
of our opinions and principles, or which points out new '*^''°'' 
methods by which we may test the correctness and con- 
sistency of our axioms. As such I consider the spirit 
infused by Kant into all modern thought. That other 
radicalism, which merely roots up, which destroys with- 
out building, which fails to find any ground of certainty, 
simply because human thought and observation may after 

VOL. I. J, 






of Romanti- 

all be a delusion,— this kind of radicalism I shall try to 
pass over as meaningless. And equally meaningless 
appear to me those opposite conservative tendencies 
which merely annul progress, which shut out the day- 
light and preach the doctrine of inertia. But this, again 
will not prevent me from recognising the real gain and 
interest which belong to some reactionary movements, 
such as lay at the bottom of Eomanticism, with its love 
of the past, its artistic idealisation of the childhood of 
mankind, of aspects of life in their infancy and primitive- 
ness, with its study of meditevalism and its more sober 
historical tastes. I shall endeavour always to ask what 
addition to the great stock of human ideas has resulted ; 
what gain we have to register ; convinced that every- 
thing that lives must grow, increase, and multiply : and 
what can be more living than Thought ? 

But although the school of Critical Thought in Kant, 
and the Komantic school as centred in Walter Scott and 
the German Romanticists, are in time almost the first 
intellectual phases of the century, they will not m the 
beginning command my special attention.^ 

of thought m the fi'-%y«»" ?* ^''^eveXor publications which mark 
r^TArlmtrU^t s^gS "^'^^ry of Lught. Of specifically 

f-lr^f ^p^ra^rEx^^tion du Syst^me du Monde.' . 
- 1799. ^vol8.)-1825. Laplace's ' Mecan.que celeste. 

1799. Legeudre's 'Th^orie des Nombres. ^ 
_ 1801. Gauss's 'DisquisitionesArithmeticaJ. 

1801. Piazzi discovers and . i„__fo " r«rps " faeini; 

''- ^St^d^r^: trL\todrof%srtionfXht/e 

published in exUniO in , 

-IROO fJauss's'Theoriamotuscorporumcoelestmm. 
i798' C^TJs . Tableau ^lementaired'Histoireuaturelle. 
I8O0I5. Cuvier's ' Lemons d'Anatomie compare. 

Though somewhat later in point of time than they, the 
school of exact research seems to have become the more 
generally recognised agent in nineteenth-century progress. 

]-al' J'»?>»'"«'^'« ' Philosophie zoologique.' 

~ '^"' ^co"vS, an7 '"'^'^^'^ '^^ ^"' <" "« electrcchemical dis- 
1802-3 Berzelius publishes his own. 

-llll Thom£*Y " " ^*" ^y***" °' ^'>""^'=*' Philosophy.' 

during '"'^'*°''»'«« father in his pajSrs, and fully expounds 

- Isns t?1 *""°"'°g yea," •» his lectures to the Royal Institution 
1808. Ma^us^announces his discovery of the polarisaLn of llghrSirough 

1802. Chladni's'Akustik.' 

1799 H.^Davy publishes his equally important 'Essay on He^t, Light. 

]lm' l^^'u^^l^ ;Recherches physiologiques/ 
l«01. Bichats 'Anatomic gendrale ' 

1799-1804 Alexander von Humboldt travels in America, and lays by 
his observations the foundation of the science^ of physical 
geography and meteorology. pnjsicai 

mVi«n«'^-f^ ""^ ^}^ Pjfosopkical movement of thought the years 
1793^806 witne^^ ,he J^/exp^^^^^^^ and 

1 7Q^ Q.? I ^ D . .} ® ^^^^ ^" *^® writings of 
llll ^ K- ^'■' ill'^^^ ^^^ a^thetische Erziehung.' 

VJl' ^<^^®^^>ng. 'Naturphilosophie.' 

17QO l^'u?".'"^' 'Transcendentalerldealismus.' 

linn f^^^^^«r°^acher, 'Reden iiber die Religion.' 

1800. Schleiermacher, 'Monologen.' 

1 / 99. Herder, ' Metakritik. ' 

Jon^ i^"^^^' * Offener Brief an Fichte.' 

1806. Hegel, ' Phtinomenologie des Geistes.' 

In b ranee — 

1804. De^unde ^Tracy's < Ideologic' represents the reigning philo- 

;'"' "!i^t:a^s':;afni?r ^" ™*'^*"<'"' ' *■•* >-«■•--« »* '•>« 

In England— 

1792-1827. Dugald Stewart's ' Elements of the Human Mind ' and his 







progress to 
be consid- 
ered first. 

To it are due the great changes in every department of 
science, of life, and probably also of literature and art, 
the great inventions and the great conflicts of our age. 
Science has not only very largely influenced our ideas, 
it has also by its applications altered the external face 
of the world we live in. It is therefore simply a tribute 
to the popular view, and a desire to start from some 
striking and generally conceded position, if I select the 
scientific movement of ideas as the first with which 
I have to deal. How has it spread in the course of 
the century ? From what beginnings and through what 
influences ? What are its principles and methods ? How 
have they themselves changed and developed ? What 
has it led to ? These are some of the questions which 

1803 'Life and Writings of Thomas Reid ' represent the predominant 

i^riod^eremv Bentham's influence, which cannot be reduced to 

Set n49«^X^s^ 'Vaust; i^^ world .n 

successive stages between the years 1790 and 1832. 

1794. Thomas Paine's ' Age of foason. ^ 

il?i4 --^ rJSfor(^w^trd .tended its influence in 

'^11 lchm:r'::d"Grthe-s -Xenien" in the • Musenalmanach.> 

1798. Schlegel's ' Athenicum.' 

1802. A.\V. V. Schlegel's Berlm lectures j^^g ^^en 

The R,ma«tic school of fiction ,<1»**;^ '° ^^"^^^J'eharacter stic of 
Frederick Schlegel uses the tf^J"/.,**^* *,"?*i^'^*eirter '(' Athenaeum,' 
a new departure in h.s revew of ^f **J„ J^^ ^ J^V aims and charac 
vol. i.) A literary movement " t*;l'^«,'l"^°Xr Tco^^ (" Lay of the Ust 
*r1",'" IsSXfhry r ThTaU? ito™ Sleri^ge C^Christabel," 

tpLffliic: ■■ iT9r:nrb:ri?^-rothe?pri7cipai wor^s of 

Goethe and Schiller (died 1805). 

I shall try to answer as concisely as possible. This 
selection does not commit me to any theory on the 
value of the scientific view as compared with other 
aspects. Such theories will have to be dealt with in a 
later portion of the work. They have sprung up in the 
course of the last hundred years, partly as the inevitable 
outcome of scientific progress itself, partly in the educa- 
tional world, where a reaction has set in against the 
undue importance which former generations attached to 
classical learning and training. I need not at present 
do more than note these opinions, nor need I define 
my position with regard to Comte's celebrated positivist 
theory on the advancing stages of the human intellect. 
Curiosity and the consensus of popular opinion suffice 
for the moment to make me take up the scientific side 
of the thought of the age. As we proceed, other directions 
and movements will present themselves, and the inter- 
dependence of all human interests will reveal and explain 40. 
what truth attaches to Hegel's celebrated doctrine of the t?i?eonhe" 
inherent dialectic of ideas, the spontaneous development d?veiop.^°"^ 

i! J.1 1 i nient of 

01 tnOUght. thought. 








It will be generally admitted that the scientific spirit is i 
a prominent feature of the thought of our century as ^S^ 
compared with gther ages. Some may indeed be in- '"'"" 
clined to look upon science as the main characteristic 
of this age. The century may thus be called with some 
propriety the scientific century, as the last was called the 
philosophical century, or as the sixteenth was termed the 
century of the Eeformation and the fifteenth the century 
of the Eenaissance. It is therefore natural that we should 
begin our study of the thought of the age with an ex- 
amination of this side of modern culture. 

It is not necessary to define what I mean by science.^ 

The use of the word science 
and its adjective scienti6c has 
varied considerably in the English 
f^nguage. We must wait for Dr 
Murray's great work to give us a 
history of the word. I venture to 
assert that it acquired its present 
definite meaning about the time of 
the formation of the British Asso- 
ciation for the Advancement of 
Science (1831). The two other 
great organisations which profes- 

sedly started for the culture of 
what we now call science — viV, 
the Royal Society for the Improve- 
ment of Natural Knowledge, and 
the Royal Institution— did not use 
the word officially in their charter 
or title, although it is used fre- 
quently in the documents and cor- 
respondence connected with the 
foundation of the younger, and 
occasionally in those referring to 
the older Society. The Royal So- 





Schools and colleges of science, triposes, examinations, 
and degrees in science, have established a popular mean- 
ing which did not exist a hundred years ago, but which 
is now well understood. For my purpose it is of some 
interest to note that the meaning of the word in French 
is somewhat different, and that the word Wissenschaft} 

ciety, and sometimea the Royal 
Inatitution, use the word "philo- 
sophy" in formal and official state- 
ments of their object. This is in 
accordance with older English 
usage. What we now universally 
call science was not infrequently 
termed in the seventeenth century 
natural knowledge, and Bacon him- 
self translates scientice by "know- 
ledge," by "learning," and some- 
times by "sciences." In France, 
on the other hand, the word " sci- 
ence" seems to have acquired its 
present meaning as far back as the 
middle of the seventeenth centurj^ 
At the time of the foundation of 
the "Academic des Sciences," in 
1666, the word was used almost in 
the same sense — embracing the 
same separate departments of know- 
ledge — as the word "science" is now 
used in this country when we speak 
of a college of science. In France, 
so far as I am aware, a cultivator 
of science has never been called a 
philosopher. Science and philos- 
ophy have there never been synony- 
mous. But science in France has 
been made to cover a larger field 
of knowledge by such adjectives as 
"moral," "social," "political," and 
has been narrowed by such other 
adjectives as "exact" and "natural," 
in the same way as the word philo- 
sophy has been more strictly defined 
in the English language by the ad- 
jectives "natural," "experimental," 
"moral," "mental," &c. At the 
head of the sciences in France stood 
" mathematics," at the base of the 

new philosophy in England stood 
"experiment" and "observation." 
^ The word Wissentchaft has a 
much wider meaning than science 
in the modern sense, and is the 
literal translation of the Latin 
scientia. It means knowledge in 
a systematic form and connected 
by some method. What the French 
call scieixce, the Germans call exacte 
Wissen8chaft. This includes mathe- 
matics and NaturtDisscnschaft, which 
covers the ground covered by the 
word "sciences" in English. The 
word Wissenschaft plays an import- 
ant part in German culture, as we 
shall see later on. The modern 
term "scientist" is about synony- 
mous with the word Naturforscker 
in German. The word savant in 
French has no synonym in English, 
but is iibout equivalent to the term 
Gelehrter in German ; and this, 
again, is partially translated by 
"scholar" in English. I suppose 
"man of science" and "scholar" 
together would be about covered by 
either savant or Gelehrter. Those 
who desire to study the older and 
modem, the English and foreign, 
uses of the word science and other 
kindred terms, should read Bacon's 
English writings ; Weld's * History 
of the Royal Society ' (1848, vol. i.) ; 
Bence Jones's ' The Royal Institu- 
tion' (1871) ; L^n Aucoc's 'L'lnsti- 
tut de France' (Paris, 1889) ; Alfred 
Maury, ' Les Academies d'autrefois' 
(vol. i., Paris, 1864) ; and the cor- 
respondence in connection with the 
foundation of the British Associa- 

by which science is translated into German, requires a 
qualification in order to cover approximately the same 
ground. These verbal differences point to differences of 2. 
thought. Only since Continental ideas and influences English and 

- . 1 . 1 Continental 

nave gained ground m this country has the word science °o*^^°« ^^ 


gradually taken the place of that which used to be 
termed natural philosophy or simply philosophy. One 
reason why science forms such a prominent feature in 
the culture of this age is the fact that only within the 
last hundred years has scientific research approached the 
more intricate phenomena and the more hidden forces 
and conditions which make up and govern our everyday 
Hfe. The great inventions of the sixteenth, seventeenth, 
and eighteenth centuries were made without special 
scientific knowledge, and frequently by persons who 
possessed skill rather than learning. They greatly in- 
fluenced science and promoted knowledge, but they were 
brought about more by accident or by the practical re- 
quirements of the age than by the power- of an unusual 
insight acquired by study.^ But in the course of the last 

tion in Dr Whewell's ' Writings and 
Correspondence' by Todhunter (2 
vols., London, 1876). I believe the 
word philosophy has lost the specific 
meaning which it acquired in the 
Baconian school, as much through 
the influence of French science on 
the one side as through that of 
metaphysics on the other. The 
latter emanated from Scotland, and 
from Germany through Coleridge. 
It reinstated the word philosophy 
in its original sense. 

^ Examples are plentiful. Not to 
speak of gunpowder and printing, 
which came earlier, we have later 
nearly all the great improvements 

connected with the manufacture of 
textiles, the fly-shuttle, the self- 
acting mule, the power- loom, the 
spinning -roller, invented by men 
of little or no scientific education. 
The same is the case with the 
older metallurgical processes, the 
refining of copper and the intro- 
duction of cast-iron. Watt was 
one of the first who brought a 
trained intellect to his mechan- 
ical work. The Royal Society was 
started with the distinct purpose 
of cultivating such knowledge as 
has "a tendency to use"; the 
Royal Institution still more so. It 
is, however, still doubtful, view- 






hundred years the scientific investigation of chemical and 
electric phenomena has taught us to disentangle the 
intricate web of the elementary forces of nature, to lay 
bare the many interwoven threads, to break up the equili- 
brium of actual existence, and to bring within our power 
and under our control forces of undreamed-of magnitude. 
3. The great inventions of former ages were made in countries 
Seni^'ind where practical life, industry, and commerce were most 
li^e. advanced ; but the great inventions of the last fifty years 

in chemistry and electricity and the science of heat have 
been made in the scientific laboratory : the former were 
stimulated by practical wants ; the latter themselves pro- 
duced new practical requirements, and created new spheres 
of labour, industry, and commerce. Science and know- 
ledge have in the course of this century overtaken the 
march of practical life in many directions.^ A confused 

ing the history of the learned 
societie's as well as the rare cases in 
which highest scientific genius is 
allied with practical skill in the 
same person, whether the cultiva- 
tion of research for its own sake 
should not preferably be kept dis- 
tinct from its hasty application. 
This is the view held by many great 
thinkers abroad. In England the 
opposite view has frequently im- 
peded the progress of pure science. 
^ A few examples may suffice. 
The discovery by Oersted and Am- 
pere of Electromagnetism (1819, 
1820) led at once to the idea of 
electrical telegraphy : the first tele- 
graph over considerable distances 
was constructed by Gauss and 
Weber (see ' Wilhelm Weber,' 
Breslau, 1893, p. 26, &c.) Tlie 
artificial preparation of an organic 
substance by Wohler in 1828 led at 
once to many attempts at prepar- 
ing expensive organic compounds — 

especially medical substances — by 
chemical synthesis. The occupa- 
tion with this problem under A. W. 
Hofmann's instructions led Perkin 
in 1856 to the discovery of the first 
anilin colour (Mauvein, see 'Ber- 
ichte der deutschen chemischen 
Gesellschaft,' No. 17, p. 3391). 
Leblanc's discovery how to make 
carbonate of soda from salt, for 
which a prize had been offered by 
the Paris Academy under Napoleon, 
led to the enormous development 
of the sulphuric acid industry in 
England and on the Continent. 
Liebig foretold in 1840 the recovery 
of sulphur from the waste of chemi- 
cal works and the effect on the 
sulphur mines of Sicily, fifty years 
before this process was satisfactorily 
carried out (see Liebig's familiar 
' Letters on Chemistry,' 1st ed., 1843, 
pp. 22, 31, &c.) But the greatest 
of all industries created in the 
laboratory was probably that of 

picture of this latest stage of culture lived in the pro- 4. 
phetic but essentially unscientific mind of Lord Bacon. LordTBa^coZ 
But he did not sufficiently allow for the amount of patient 
scientific toil that was needed, nor for the time which the 
preparation of the instruments of research would require, 
nor for the necessity of destroying existing superstition 
and accumulated errors. All that has since been done by 
Newton and the great Continental mathematicians in the 
former, and by Bayle and Voltaire in the latter sense. 
Bacon had hoped to achieve at once by the new philo- 
sophy of fruit and progress. Such expectations were 
inevitably doomed to disappointment, though posterity 
has made amends by all but universally referring to him 
as the pioneer of modern thought, — as the herald of a 
new era of human civilisation.-^ 

making artificially the fertilising 
compounds required in common 
agriculture which followed on the 
publication of Liebig's famous work 
on 'Chemistry in its applications 
to Agriculture and Physiology' in 
1840 (see Hofmann's Faraday 
Lecture of 1875, 'The Lifework of 
Liebig,' p. 15, &c.) Liebig also 
discovered and described in 1832 
the properties of chloroform and 
chloral, fifteen years before Simpson 
introduced the first as an anaesthetic 
and twenty years before Oscar 
Liebreich discovered the physiolog- 
ical action of chloral (ibid., p. 101, 
&c.) Sir Lowthian Bell calculated, 
many years before the invention 
of the so-called basic process of 
making steel, the fertilising value 
of the phosphorus which was con- 
tained in the ironstone of Cleve- 
land, and which then made it use- 
less for the manufacture of high- 
class iron and steel. The great 
revolution in the theory of the 

steam-engine embodied in the work 
of Macquorn Rankine is to be traced 
back to the patient measurements 
by Joule of the mechanical equiva- 
lent of heat. 

^ A great controversy arose on 
this subject through the publica- 
tion of Liebig's pamphlet in 1862, 
entitled, ' Francis Bacon von Veru- 
1am und die Methode der Natur- 
forschung.' It was directed mostly 
against the exaggerated view taken 
by Macaulay in his celebrated essay. 
The fact is that Bacon, like Vol- 
taire after him, was much more 
of an essayist and a man of the 
world than a patient labourer in 
any special field of research ; he 
was more of a philosopher in a 
worldly sense (what the Germans 
call " ein Weltweiser ") than a pro- 
found thinker. He misunderstood 
many of the great discoveries of his 
age, though he prophetically fore- 
saw the great change in the spirit 
of inquiry. He did not appreciate 






Defect in 


Our age has in many ways inherited the spirit of 
Bacon's philosophy ; but it would be a mistake to attri- 
bute its great scientific achievements to the exclusive 
working of this spirit. Bacon was neither a retired and 
patient nor an accurate thinker — the desire to apply and 
make his learning useful led him away from the " sapien- 
tum templa serena " into the forum of life : in his own 
experience, as well as in his writings, he anticipated many 
of the dangers which beset modern culture — the love of 
premature application, and the haste for practical results 
and achievements. Science, which in the hands of patient 
and diligent observers ^ had just been rescued from the 
sway of empty metaphysical and theological reasoning. 

the enormous part which mathe- 
matics would play in the develop- 
ment of science. In this respect 
Descartes was a genius of much 
greater originality — his actual con- 
tributions to scientific progress, as 
well as those of Pascal, being far 
beyond those of Bacon ; but they 
both retained the metaphysical 
habit of thought which has char- 
acterised many, if not all, among 
the greatest mathematicians. In 
modern culture the popularisation 
of novel views and ideas has become 
so important a factor that writers 
like Bacon and Voltaire, who com- 
bine the scientific and literary taste, 
are of the greatest importance in 
the diflFusion of new ideas, though 
none of their works need be looked 
upon as great repositories of re- 
search and knowledge. Before Lie- 
big wrote his pamphlet, a very im- 
partial and temperate estimate of 
Bacon's philosophy and its relations 
to actual science was published by 
Robert Leslie Ellis in his introduc- 
tion to the philosophical works of 
Lord Bacon (London, 1857). As 

the literature of the subject is so 
large, I cannot but recommend this 
essay as containing one of the best 
discussions of it. 

^ A very good and concise account 
of the achievements of these con- 
temporaries and forerunners of Ba- 
con—of Tycho (1546-1601), Kepler 
(1571-1630), Galileo (1564-1642), 
Gilbert (1540-1603), Harriot (1560- 
1621), Napier (1550-1617), Harvey 
(1578-1656) — is given by John 
Nichol in the second volume of his 
' Francis Bacon, his Life and Philo- 
sophy' (Edinb., 1889), pp.-86, 254. 
In the same volume (p. 193) there 
is also a useful summary of Bacon's 
real claims to a place among physi- 
cists, of his ignorances (p. 196), and 
of the reception which his works 
met with in England and abroad 
(p. 233 to end). Not quite feo read- 
able, but more complete, isT' the 
little volume of Hans Heussler, 
* F. Bacon und seine geschichtliche 
Stellung' (Breslau, 1889), with its 
flood of references — which exhaust 
the subject. See especially p. 160, 
&c. , on Bacon's anticipations. 

was in danger of falling a prey to hasty generalisation 
for the purpose of practical ends. Practical demands 
threatened then, as they frequently still do, to stifle or 
to force into premature growth the patient thought which 
had just begun to germinate in the new light and freedom 
of reason. The narrow view had indeed been widened, 
and the breadth of the land had been surveyed, but there' 
was little inclination to deepen the view, or to do more 
than search on the surface. (The spirit of Bacon's philo- 
sophy required a corrective. For a long time to come the 
hope of practical application had to be postponed ; the 
thmker and student had to retire into solitude, and there 
to lay the more permanent foundations of the new re- e 
search. This was done by Newton for all time. His S"^^. 
reputation spread more slowly than that of the great 
High Chancellor; but it rests on a surer foundation, 
which baffles every attempt to shake it, and will outlast 
all coming changes of thought.") 

The beginnings of modem scientific thought are thus to 
be found in this country. Lord Bacon foretold propheti- 
cally the great change which the new philosophy was 
destined to work. Newton more patiently drew up the 
first simple rules and gave the first brilliant application. 
More than the unfinished and wearisome pages of Bacon's 
'Novum Organum' does the 'Principia' deserve to be 
placed on a line with Aristotle and Euclid as a model 
work of scientific inquiry. 

Por a real recognition of the greatness of Newton, as well 7 
as for a partial realisation of Bacon's plans, we are, however nIX'^'s"" 
mainly indebted to the French philosophers of the second £C 
half of the eighteenth century. Bacon's plan of promoting ««'p^«^'"'" 





Bacon and 

knowledge and research by the co-operation of many was 
more thoroughly realised in the old French Academy 
than in the Koyal Society of London : his desire to unite 
all knowledge in a collective work underlies the great 
productions of Bayle, and still more those of the Ency- 
clopaedists. The many problems contained in Newton's 
*Principia' were first treated singly by Clairault and 
Maupertuis; a general knowledge of his view of the 
universe was introduced into popular literature by Vol- 
taire,^ who made use of it as a powerful weapon wherewith 
to combat error and superstition, or, as he termed it, " pour 
^eraser I'infame"; but for a full announcement of its 
scientific value and its hidden resources we are indebted 
to Laplace, whose * M^canique celeste' was the first 
comprehensive elaboration of Newton's ideas, and whose 
*Systeme du Monde' became the scientific gospel of a 
whole generation of Continental thinkers. 

We may look upon Lord Bacon as one who inspects a 
large and newly discovered land,^ laying plans for the 

1 I believe Voltaire was the author 
of the term Neictonianisme. The 
modesty and truly scientific spirit 
of Newton would not have allowed 
him to apply such a term to his 
work, and it is doubtful whether 
Voltaire did not extract from 
Newton's ' Philosophia Naturalis ' a 
general philosophy which was not 
conceived in his spirit. 

2 Cowley in his Ode to the Royal 
Society : — 

•'Baconatlast, a mighty man, arose, . . . 
And boldly undertook the injur'd pupil's 

... led us forth at last, 
The barren wilderness he past ; 

Did on the very border stand 

Of the blest promis'd land ; 
And, from the mountain's top of his ex- 
alted wit, 

Saw it himself, and shew'd us it." 

On this Mr Ellis remarks (Bacon's 
Works, vol. i. p. 63) : " Bacon has 
been likened to the prophet who, 
from Mount Pisgah, surveyed the 
Promised Land, but left it for others 
to take possession of. Of this happy 
image, perhaps part of the felicity 
was not perceived by its author. 
For though Pisgah was a place of 
large prospect, yet still the Prom- 
ised Land was a land of definite 
extent and known boundaries, and, 
moreover, it was certain that after 
no long time the chosen people 
would be in possession of it all. 
And this agrees with what Bacon 
promised to himself and to man- 
kind from the instauration of the 
sciences. ... In this respect, as in 
others, the hopes of Francis Bacon 

development of its resources and the gathering of its 
riches. But the wealth lies deep down, and is only indi- 
cated by the first labours of the early pioneers. Newton, 
following these, unites their beginnings into a systematic' 
exploration, and sinks the main shaft which reaches the 
lode of rich ore. He opens out the wealth of the mine 
and marks out the work for his followers. But many 
difficulties had to be overcome, much united effort and 
a vast organisation of labour were required, in order to 
develop to the full Newton's scheme, and to raise the 
great treasure which he had reached. This was not done 
until the end of the last century, when Laplace collected, 9 
arranged, and condensed the work of French and English ^o?^''' 
mathematicians and observers into a picture of the uni- 
verse. A variety of circumstances had combined to make 
the French capital the place above all others where the 
means and materials for the development of the great 
work could be most easily procured. Let us glance for 
a moment at the different factors in operation during 
the eighteenth century which contributed to the great 

Whilst Newton was labouring privately and almost 
unassisted 1 at the greatest scientific work produced in 

were not destined to be fulfilled. 
It is neither to the technical part 
of his method, nor to the details of 
his view of the nature and progress 
of science, that his great fame is 
justly owing. His merits are of 
another kind. They belong to the 
spirit rather than to the positive 
precepts of his philosophy." 

^ It has been stated that New- 
ton, not knowing of Norwood's ap- 
proximately correct determination 

of the length of a degree in 1635 
(published in his 'Seaman's Prac- 
tice' in 1637), but relying on the 
old figure of sixty miles for a de- 
gree of latitude (confirmed by Ed. 
Wright, Cambridge, 1610), was led 
away from the right supposition, 
which he entertained as far back as 
1665, regarding the moon's orbit, 
and had to wait for Picard's figures 
(ascertained about 1669, published 
in France about 1672, and in the 




modern times by any single mind,^ the penetrating and 
far-seeing genius of Colbert had already recognised the 
important part which science would one day play in 
the government of the world, and had secured the ap- 
proval of his royal master to the constitution of an Aca- 

Philos. Transactions in 1675), by 
applying which he determined that 
" the moon appeared to be kept in 
her orbit purely by the power of 
gravity." See Brewster's 'Life of 
Newton,' vol. i. p. 290, &c.; Tod- 
hunter's ' History of the Theories of 
Attraction,' vol. i. p. 38, &c. This 
account is, however, now discredited 
(see infra^ chap, iv.) For the part 
which Dr Hooke and Halley took in 
the discovery of the "reciprocal 
duplicate " ratio, see also Brewster, 
loc. cit., vol. i. p. 291, &c. During 
the writing of the*Principia' New- 
ton carried on a useful correspond- 
ence with Flamsteed, who was then 
Astronomer-Royal. How this happy 
co-operation ceased ten years later 
can be read at length in Brewster 
{loc. cit.y\o\. i. p. 312 ; vol. ii. p. 164, 
&c.) The greatest material assist- 
ance which Newton received was 
from Halley, who defrayed the ex- 
penses of publishing the * Principia,' 
after the Royal Society, to which it 
was dedicated, had reversed its resol- 
ution to defray them (Brewster, vol. 
i. p. 305, &c.) Nevertheless Weld, in 
his 'History of the Royal Society,' 
says : " Fortunate indeed was it for 
science that such a body as the Royal 
Society existed, to whom Newton 
could make his scientific communi- 
cations ; otherwise it is very possible 
that the ' Principia ' would never 
have seen the light." Though one 
must lament the diflferences be- 
tween Flamsteed and Newton, which 
prevented the latter from bring- 
ing his investigations of the lunar 
and planetary theories to a close 
(Brewster, vol. i. p. 312), a word of 

deep gratitude is due to Flamsteed's 
own exertions in the cause of astro- 
nomy. After Charles II. had built 
the Observatory in order to have 
the places of the fixed stars ' ' anew 
observed, examined, and corrected 
for the use of his seamen " (Flam- 
steed, History of his own Life), and 
after he had appointed Flamsteed 
Astronomer -Royal at a salary of 
£100 per annum, the Observatory, 
" hurriedly established, was left for 
a period of nearly fifteen years 
without a single instrument being 
furnished by the Government" 
(Weld, vol. i. p. 255). The instru- 
ments were mostly supplied by 
Flamsteed himself or lent by others, 
and besides, " the king had ordered 
that Flamsteed should instruct 
monthly two boys from Christ 
Church Hospital, which was a great 
annoyance to him, and interfered 
with his proper avocations " (Baily, 
• Account of the Rev. J. Flamsteed'). 
"Any other man would probably 
have succumbed under the amount 
of drudgery appertaining to the 
office (earning his salary by labour 
Jiarder than thrashing), if indeed, 
in the absence of encouragement, 
he would have continued in it at 
all, and particularly when the re- 
ward was so insignificant" (W^eld, 
vol. i. p. 256). 

^ "And it may be justly said, 
that so many and so valuable Philo- 
sopliical Truths, as are herein dis- 
covered and put past dispute, were 
never yet owing to the Capacity 
and Industry of any one Man " 
(Words of Halley, Philos. Transac- 
tions, vol. xvi., 1687). 


demy, which was based upon the endowment of research 
and which prompted the co-operation of its members in 
organised ' scientific work. Whilst the Eoyal Society of 
London only received a charter, and existed by the en- 
trance payments and contributions of its own members 
augmented by private donations, the Paris Academy had' lo 
as far back as 1671, received the funds with which t J IS^dty 
commence its labours in connection with the survey of ''"'""'''* 
the kingdom and its extensive dependencies. It was these 
labours which led to the measurements of the length of 
the seconds pendulum, and of the variation of gravity in 
different latitudes ; to the explanation of this variation 
by Huygens ; to the controversy regarding the figure of 
the earth ; to the direct measurements of the arcs of the 
meridian in Peru and Lapland ; and, finally, to Clairault's 
celebrated work on this subject.^ It was almost exclu- 
sively by these observations that the data were found 
with which to substantiate Newton's mathematical reason- 
ings : in his own country that fruitful co-operation which 

" Le roi assurait I'existence des 
Acaddmiciens par des pensions et 
mettait lib^ralement h leur disposi- 
tion un fonds destine h pourvoir aux 
frais de leurs experiences et de leurs 
mstruments " (Maury, * Les Acade- 
mies d'autrefois,' vol. i. p. 13). Or- 
ganisation and co-operation are diffi- 
cult to obtain in societies founded 
on private and voluntary contribu- 
tions. In England they scarcely ex- 
isted before the foundation of the 
British Association, with perhaps 
one illustrious exception pointed 
out by Struve ('Description de I'Ob- 
servatoire de Pulkowa,' 4to, P^ters- 
bourg, p. 5) : " H y », dans I'histoire 
de 1 observatoire de Greenwich, un 
point tr^s remarquable, savoir que 

les astronomes ont travaille sur 
un meme plan, depuis I'origine de 
I'etablissement jusqu'k I'epoque 
actuelle." Organisation and co- 
operation were the order in the 
Paris Academy from the beginning. 
" On y travaillait de concert " ; and, 
"D^s les premiers mois de 1667,' 
Perrault proposa un plan de travail 
pour la physique, c'est h dire pour 
1 ensemble de I'histoire naturelle " 
(Maury, loc. cit., p. 15). 

^ A full account of these is given 
in Todbunter ('Hist, of Theories of 
Attraction, &c.,' vol. i.) Clairault's 
book was published in 1743, and had 
the title, ' Thdorie de la Figure de 
la Terre, tir^e des Principes de 
I'Hydrostatique, par Clairault.' 




methods in 

can only be secured by an academic organisation and by 
endowment of research was wanting. No one since the 
time of Bacon had been more impressed with this neces- 
sary condition of modern progress than Newton's great 
rival, Leibniz,^ much of whose time was spent in pro- 
moting academies all over Europe — in Berlin, St Peters- 
burg, Dresden, and Vienna — and who had himself been 
early attracted to Paris and London by the scientific 
fame of their learned societies, though he significantly 
pointed out the want of activity and efficiency in the 
early history of the Eoyal Society. 
^ There was, moreover, another and independent line 
of scientific thought which had centred in France, 
the development of which came greatly to the aid of 
the students of Newton's work. This was the purely 
mathematical elaboration of the various infinitesimal 
methods of the French and English mathematicians, by 
which they were all brought together, simplified, and 
united into a calculus with strict rules, a practical nota- 
tion, and an easy algorithm. Newton himself had for the 
purposes of his great work invented a new and powerful 

1 A collection of Leibniz's writ- 
ings on this subject will be found 
in the 7th volume of M. Foucher de 
Careil's edition of Leibniz's Works, 
Paris, 1875. Of the projects of 
Leibniz, only the Academy of Berlin 
came into existence during his life- 
time (1700 and 1701); the others 
were discussed at great length with 
the Elector of Saxony, with the Em- 
peror, and with Peter the Great. 
The Academy of St Petersburg was 
founded in 1724, eight years after 
the death of Leibniz. The Academy 
of Vienna did not come into life till 

1846, and in the same year that of 
Saxony was founded, which has its 
seat at Leipsic. Leibniz had the 
largest views on academic life and 
work : they were to embrace the 
historical and philosophical studies 
as well as the purely scientific, and 
were to stand in relation with the 
higher and lower educational in- 
stitutions. His ideas are beet 
realised at Berlin. See Jacob 
Grimm's interesting discourse, en- 
titled ' Ueber Schule Universitat 
Akademie' (Kleine Schriften, vol. 
i. p. 211, &c.) 


instrument, afterwards called " the method of fluxions " ; 
but he had not made it generally known before the' 
invention of Leibniz was published.^ This, though much 
later in time, had been perfected and applied by his 
friends and followers in a most extensive manner, and 
had, in fact, become the recognised mathematical ' lan- 
guage of the Continent. No learned body did more than 
the Paris Academicians to perfect (with purely scientific 

^ Leibniz seems to have been in 
possession of his method as early 
as 1675, and communicated it to 
Collins in 1677. It was, however, 
not published before 1684 in the 
'Acta Eruditorum,' and then prob- 
ably only on account of some writ- 
ings of Tschirnhausen trenching on 
the same subject. Newton seems 
to have been in possession of his 
methods as early as 1665, fully ten 
years before Leibniz made use of 
his. Immediately after the publi- 
cation of Leibniz's paper in 1684, 
the differential calculus was taken 
up by the Continental mathema- 
ticians, especially by James Ber- 
noulli (1654-1705) and John Ber- 
noulli (1667-1748), and the Mar- 
quis de I'Hopital, who published 
the first treatise on the new calculus 
in 1696. Newton did not publish 
any account of his method, though 
he must have used it extensively in 
arriving at the results contained 
in the 'Principia.' Different views 
have been expressed on the reasons 
which induced Newton to withhold 
from publication his new methods, 
and the question to what extent 
Leibniz owed the first suggestions 
of his method to Newton remains 
also undecided. Those who take 
an interest in the personal question 
should refer to the original docu- 
ments, the * Commercium Epistoli- 
cum,' published by the Royal Society 
in 1715 ; the pamphlet of Gerhard t. 

Die Erfindung der Differential- 
rechnung' (Halle, 1848). An ex- 
treme view, unfavourable to Leib- 
niz's originality, is taken by Sloman, 

Leibnitzens Anspruch auf die 
Erfindung der Differentialrech- 
nung' (Leipzig, 1857); but it has 
not been generally adopted by those 
who have examined into the subject. 
As to the superiority of the Conti- 
nental notation for practical pur- 
poses, this seems to have been 
generally admitted at the beginning 
of this century, when it was intro- 
duced into English mathematical 
works. In the school of W. R. 
Hamilton of Dublin the notation 
used by Newton acquired a peculiar 
importance, and it is still occasion- 
ally used in some important works 
like Tait and Steele's 'Dynamics 
of a Particle,' and Thomson and 
Tait's 'Natural Philosophy.' See 
on this Tait's article on Hamilton in 
the 'North British Review ' (Sept. 
1866). The importance of the 
labours of the Continental school, 
headed by Leibniz, for the diffusion 
of the new methods, is well de- 
scribed by Remont de Montmort in 
a letter to Brook Taylor, dated 18 th 
December 1718, and given in the 
appendix to Brewster's *Life of 
Newton ' (vol. ii. p. 511, &c.) Those 
who take more interest in the fate 
of ideas and the progress of thought 
than in personal matters will do 
well to read this letter. 









interest) this new calculus, which in the course of the 
eighteenth century had in the hands of Lagrange been 
adapted to all the purposes and problems contained or 
suggested in Newton's * Principia/ 

This leads me to a third and yet more important element 
of scientific thought, which was peculiar to the Continental, 
and especially to the French mathematicians, counting 
among them Leibniz, who, though a German, was wholly 
trained in the French school. This factor is the estab- 
lishment of pure mathematics on an independent founda- 
tion, and the cultivation of research into the abstract 
relations of quantity, without reference either to geomet- 
rical or mechanical problems and applications. It is 
the modern analytical spirit introduced by the great 
French algebraists of the seventeenth century, which 
looks upon geometry, mechanics, and astronomy merely 
as "questions d'analyse," and makes their solutions de- 
pend upon the perfecting of an abstract calculus rather 
than on the study of these individual problems them- 
selves. Opposed to this spirit of analysis, which in 
general seeks the solution of any given question by 
looking upon it as a special case of a wider and more 
abstract problem, is the method known to the ancients, 
which never loses sight of the actual application, be it a 
figure in geometry or a special arrangement of physical 
forces, and is more interested in the peculiarities of the 
individual case than in the abstract formula of which it 
may be considered an application. This opposite view 
regards the calculus and mathematics in general merely 
as an instrument, the value of which lies solely in its 
application to real physical problems. It is usually 

termed the synthetical method, and has in modem times - is. 
survived principally in England, where inductive reason- SetTcaT" 
ing, based upon observation of detail, has since the age "''"'"''^ 
of Lord Bacon been most successfully cultivated.^ These 
different ways of approaching the same subject will fre- 
quently engage my attention in the course of this survey : 
the greatest mathematicians of modern times have recog- 
nised the importance of both aspects, and the enormous 
progress of the science itself has depended, no doubt, on an 
alternating employment of them. Leibniz clearly foresaw 
this when, in his correspondence with Huygens and others, • 
he urged the necessity of not abandoning the purely geo- 
metrical view, or entirely sacrificing the older for the 
modern methods.^ There can, however, be no doubt that 

^ See on this point the opinion of 
an authority, Hermann Hankel, in 
his highly interesting and sugges- 
tive lecture, ' Die Entwickelung der 
Mathematik in den letzten jahr- 
hunderten' (Tiibingen, 1869, re- 
published by P. du Bois-Reymond, 
1884). Speaking of the age of 
Leibniz he says : "Though on the 
Continent mathematicians were not 
80 conservative as in England, where 
a purely geometrical exposition was 
considered to be the only one worthy 
of mathematics, yet the whole spirit 
of that age was directed to the sol- 
ution of problems in geometrical 
clothing, and the result of the cal- 
culus had mostly to be retranslated 
into geometrical forms. It is the in- 
estimable merit of the great mathe- 
matician of Basel, Leonhard Euler, 
to have freed the analytical calculus 
from all geometrical fetters, and 
thus to have established analysis 
as an independent science. Analy- 
sis places at its entrance the con- 
ception of a function, in order to 
express the mutual dependence of 

two variable quantities. . . . The 
abstract theory of functions is the 
higher analysis. . . . The concep- 
tion of a function has been slowly 
and hesitatingly evolved out of spe- 
cial and subordinate conceptions. 
It was Euler who first established 
it, making it the foundation of the 
entire analysis, and hereby he in- 
augurated a new period in mathe- 
matics" (p. 12, &c.) 

2 To Huygens, 16th September 
1679 : " Je ne suis pas encor con- 
tent de I'Alg^bre, en ce qu'elle ne 
donne ny les plus courtes voyes, ny 
les plus belles constructions de Geo- 
metric. . . . Je croy qu'il nous faut 
encor une autre analyse proprement 
gdom^trique ou lineaire, qui nous 
exprime directement situm, comme 
I'Alg^bre exprime magnitudinem. 
Et je croy d'en avoir le moyen, 
et qu'on pourroit reprdsenter des 
figures et mesures des machines et 
mouvements en caract^res, comme 
I'Algebre represente les nombres 
ou grandeurs" (Leibniz, Mathem. 
Werke, ed. Gerhardt, vol. ii. p. 19). 






of science 
on French 

the great success which attended Laplace's work, the 
elaboration of a system of the universe out of the prin- 
ciples of Newton, was largely due to the perfection which 
the analytical methods had gained in the hands of his 
predecessors, and to the skill with which he himself re- 
duced the several problems to purely analytical questions. 
But however much exact methods, learned societies, 
and regal endowments may do to promote the growth of 
the scientific spirit, experience has shown that popular 
favour and interest furnish a still more effective stimulus. 
Even the most abstract reasonings of the mathematician 
require to be brought into some connection with the gen- 
eral concerns of mankind, before they can attract talent 
from outside, or enter into that healthy action and reaction 
which are the soul of all mental progress. In this respect, 
also, France during the second half of the eighteenth cen- 
tury was far in advance of other countries. No other liter- 
ature of that age can be compared with that of France, when 
we look at the influence or the expression which modern 
scientific views and interests had already attained in it ; 
and no other country could at the end of the eighteenth 
century boast of such splendid means of scientific instruc- 
tion as then existed in Paris. In two important depart- 
ments — the popularisation and the teaching of science — 
France for a long period led the way.^ A general inter- 


To Bodenhauseii (about 1690) : " I 
am of opinion that in the problems 
of ordinary Geometry the metkodus 
Veterum has certain advantages 
over Analysin Algehraicam, and I 
think I have remarked to you that 
there remains an A nalysis geometricE 
propria, toto cceIo ab Algebra diversa 
et in mtdtis longe Algebra compendio- 

sior utiliorque" (ibid., vol. vii. p. 
359). " It is certain that algebra, 
by reducing everything a situ ad 
solam magnitudinem, hereby very 
frequently complicates things very 
much" (p. 362). 

^ Perhaps it would be more cor- 
rect to say that science was fashion- 
able than that it was popular in the 

est was thus created in the proceedings and debates of the 
Academy, and the discoveries of its illustrious members 
found their way into the lectures and text- books of the 
professors. Whatever eminence German science may have 
gained in this century, from a purely literary point of 
view, through the works of A. von Humboldt, or English 
science through those of Darwin, the history of both 
literatures during the eighteenth century can be written 
almost without any reference to science at all — so small 
was the direct influence of such giants as Newton and 
Leibniz on the popular mind. But who could exclude 
from a history of the elegant literature of France the 
names of Voltaire, of Buffon, of D'Alembert, or of Con- 
dorcet ? These form a connecting link between science 
and general literature.^ A study either of English or 

eighteenth century in France. But 
it became popular through the in- 
fluence of the great schools of Paris. 
Before becoming popular with the 
masses it became so in cultivated 
and literary circles. The result 
has been that science in France 
alone has attained to a perfect form 
of expression. Whereas in other 
countries the great models of origi- 
nal research and thought were writ- 
ten in the severe style handed down 
by the ancients (Newton's 'Prin- 
cipia ' and Gauss's * Disquisitiones 
Arithmeticse '), the great work of 
Lagrange (the 'M^anique analy- 
tique') is a model of literary style 
in the modern sense. Science in our 
age has become popular through 
its applications. It is the utili- 
tarian spirit that has popularised 
science in Germany and England. 
In France alone science, before com- 
ing under the influence of the utili- 
tarian, came under that of the lit- 
erary spirit. It was the influence of 

the academies that brought this 
about. See Maury, 'Les Acade- 
mies d'autrefois,' vol. i. p. 178, &c. 
More than with Richelieu, the in- 
terest in science nowadays is un- 
fortunately only too often purely 
" metallic " (quoted from Lord 
Chesterfield's Letters). See also 
on the literary as compared with 
the modern practical character of 
science, Maury, ibid., p. 161. 

^ "On erigeait meme en prin- 
cipe la n^cessitd pour un philosophe 
de ne rester Stranger h aucune 
science. * L'esprit philosophique 
fait tant de progres en France de- 
puis quarante ans,' ^crivait Voltaire 
h madame Du Ch^telet, en lui d^- 
diant sa trag^die d'Alzire, 'que si 
Boileau vivait encore, lui qui osait 
se moquer d'une femme de condi- 
tion, parce qu'elle voyait en secret 
Roberval et Sauveur, il serait oblig^ 
de respecter et d'imiter celles qui 
profitent publiquement des lumieres 
des Maupertuis, des Reaumur, des 






Absence of 
this influ- 
ence in Eng- 
land and 


Schools of 
science in 

of German eighteenth-century literature does not intro- 
duce one to the great controversies of science, but a 
study of Voltaire leads one into the midst of the pro- 
found problems of the Newtonian and Cartesian philo- 
sophy, the disputes on the correct measure of force.^ 
Buffon's influence, also, by spreading a taste for the study 
of nature and by making objects of natural history attrac- 
tive, was probably much more important than his actual 
contributions to the natural sciences themselves.^ 

For the growth and diffusion of the scientific spirit 
itself, the great schools in Paris were even of greater 
value than the popular writings of Voltaire and Buffon. 
Most of the Academicians were trained in these schools, 

and many of them taught there for many years.^ It was 
with a true insight into the higher intellectual needs of 
the nation that the successive Governments of the Eevo- 

Mairan, des Du Fay et des Clairault ; 
de tous ces veritables savants qui 
n'ont pour objet qu'une science 
utile, et qui, en la rendant agreable, 
la rendent insensiblement neces- 
saire h, iiotre nation. Nous sommes 
au temps, j'ose le dire, oil il faut 
qu'un poete soit philosophe et oil 
une femme peut I'etre hardiment.' 
En parlant ainsi, Voltaire ne faisait 
qu'exprimer I'opinion de son siecle, 
et ambitieux lui-meme de reuuir le 
titre de geom^tre h. celui de poete et 
d'historien, il s'etait fait expliquer 
parmadame Du Chatelet la physique 
de Newton " (Maury, * Lea Acad, 
d'autrefois,' vol. i. p. 156). 

^ See Maury, vol. i. p. 157, &c. ; 
and Du Bois-Reymond, " Voltaire 
als Naturf orscher " in * Gesammelte 
Reden,' vol. i. p. 1. 

2 "Sans r^loquence de Bufifon, 
la zoologie serait demeuree encore 
longtemps le privilege d'un petit 
nombre ; elle eut laiss^ indifferents 
ceux que la nature ^meut moins que 
le charme de la parole. La vieille 
education classique avait le tort 
de nous laisser tres-ignorants des 
choses du monde cree. Buffon com- 

muniqua aux sciences le charme des 
lettres. La curiositd s'eveilla, et en 
1760, Valmont de Bomare put ouv- 
rir a Paris le premier cours d'his- 
toire naturelle ; il fut assidument 
suivi " (Maur5% vol. i. p. 283). A. 
von Humboldt had a similar influ- 
ence in Berlin seventy years later. 
See Du Bois-Reymond, loc. cit.y 
vol. i. p. 510. Guardia, * Histoire 
de la Medecine* (Paris, 1884), says 
of Buffon, " Fontenelle avait rendu 
la science aimable et accessible. 
Buffon I'associa a la philosophie et 
aux lettres et I'introduisit defini- 
tivement dans la soci^te " (p. 384). 
What a contrast, when we read in 
the * Life of Sir W. R. Hamilton ' 
(by R. P. Graves, vol. ii. p. 196) 
that Dr Buckland's communica- 
tion at the Bristol meeting of the 
British Association (1836) " was 
apparently the first occasion of 
bringing before the public mind in 
England the geological doctrine of 
the great antiquity of the earth ; 
for out of the expressly scientific 
circles, very little — you [viz.. Count 
Adare] are aware — is known of 
what scientific men are about " ! 

^ Before the age of the Revolu- 
tion, which did so much to pro- 
mote higher scientific education, 
Paris possessed already many great 
schools. First in importance was 
the College de France, founded in 
1530 by Francis I. Gassendi and 
Roberval taught there in the 
seventeenth century, and about 
the middle of the eighteenth cen- 
tury science began to be more ex- 
tensively represented, Lalande and 
Daubenton, occupying chairs. The 
College et Ecole de Chirurgie was an 
ancient establishment. There was 
the Jardin des Plantes, with Buffon, 
Lemonnier, ,Daubenton, and Four- 
croy ; the Ecole royale des Mines, 
founded in 1783, where Puhamel 
taught metallurgy ; the Ecole des 
Fonts et Chaussees, founded by 
Turgotin 1775. Daubenton, Four- 
croy, and Vicq d'Azyr taught in 
the Ecole v^t^riuaire d'Alfort, 
founded in 1766. Besides the 
Acaddmie des Sciences, the Acadd- 
mie royale de Chirurgie, founded 
by Lapeyronie under Louis XV. in 
1731, had a great influence on the 
development of anatomy and sur- 
gery during the eighteenth centur}^ 
Tenon and Petit, as well as Quesnay 
the economist, were amongst its 
members, and it kept up a lively 
intercourse with anatomists all over 
Europe. The Paris academies had 
also their representatives and con- 
nections in the provinces. Inde- 
pendent academies of science were 
affiliated with the Acaddmie des Sci- 
ences — 1716 at Bordeaux, 1706 at 
Montpellier, 1746 at Toulouse, 1766 
at Bdziers. Before having received 
their lettres patentes, which gave 
their members certain privileges, 
most of these academies had exist- 
ed as independent societies. Other 

provincial academies, such as Aries 
(1668), Nimes (1684), Soissons 
(1674), MarseiUes (1726), were affili- 
ated with the Acaddmie fran9aise. 
Others, such as Caen (1705), Lyons 
(1724), Dijon (1740), Rouen (1744), 
Amiens and Nancy (1750), Besan- 
9on (1757), Metz (1760), Clermont 
(1780), Orleans (1786), were not 
specially affiliated. These dates 
show how very much earlier a 
literary and scientific organisation 
existed in France than in other 
countries. The Protestant univer- 
sities in Germany formed an or- 
ganisation of a different kind, with 
which I shall deal later on. The 
academic system, so early developed 
in France, was of great use to the 
culture of the sciences. French 
science is usually considered to be 
almost entirely located in Paris. 
M. Bouillier ('L'lnstitut et les 
Academies de Province,' Paris, 
1879) has drawn attention to the 
great services of this network of 
academies. Many of the most emi- 
nent writers belonged to these pro- 
vincial centres, and worked for 
them even after becoming members 
of the more celebrated academies. 
Montesquieu is connected with Bor- 
deaux, Cassini and many eminent 
doctors with Montpellier, Dijon has 
the honour of bringing out Rous- 
seau, and Toulouse gave prizes to 
Bossut and Clairault. Robespierre's 
name is connected with the Academy 
of Arras, Marat discourses at Rouen 
and Lyons on electricity and optics, 
and Dan ton and Bonaparte compete 
for the prix Raynal at Lyons. 
" Mais," says M. Bouillier, " ce qui 
nous semble le plus digne de 
remarque et d'dloge, ce sont les 
ecoles gratuites de dessin, les cours 
gratuits de physique, de chimie, 






lution, in the midst of the more pressing problems of 
national safety and welfare, betook themselves to the 
solution of the great problem of national education and 
the instruction of all grades of society. "The Convention," 
says the historian of public instruction,^ " affords us the 
strange and grand spectacle of an assembly, which on the 
one side seems to have no other mission than to crush in 
the name of public welfare everything that stands in the 
way of the triumph of the Eepublican State, and which 
by Govern- can SCO uo othcr way of attaining this than the most 
Revolution, terrible and cruel of tyrannies ; and which on the other 
side devotes itself, with a stoical calm and serenity, form- 
ing a surprising contrast to its acts, to the study, the 
examination, and the discussion of all the problems in- 
volved in public instruction, of all the measures con- 
ducive to the progress of science. It had the glory of 
creating institutions, some of which were carried away by 
the blast of the Kevolution, but among which the most 
important still exist for the great honour of France, and 
bear proof of the loftiness of her ideas." ^ 

dTiistoire naturelle, d'anatomie, 
d'antiquites, fondes par un certain 
nombre d'academies et,entre autres, 
par Dijon, par Rouen, par Bordeaux, 
par Toulouse, par Montpellier, et 
dont les professeurs ^taient des 
membres, non retribues de ces 
academies. ... A combien de 
jeunes talents les academies provin- 
cialea n'ont-elles pas donn^ I'essor, 
par leurs recompenses solennelles et 
leurs encouragements ? Combien de 
leurs laureats ne sont pas devenus 
des hommes c^l^bres?" (p. 81, &c.) 
Besides Bouillier, consult on these 
matters the several articles, " Aca- 
ddmie," "College," "Ecole," in the 
* Grande Encyclop^ie.' 

1 C. Hippeau, ' L'Instruction pub- 
lique en France pendant la Revolu- 
tion,' 1® s^rie, preface, p. xix. 

- It appears nowadays a kind of 
paradox that, as M. Hippeau re- 
marks, in the very year 1793, when 
"the Convention was labouring 
with a feverish ardour at the crea- 
tion of schools of all degrees," this 
same Convention, on a report of the 
Committee of Public Instruction, 
vo.ted on the 8th of August the 
suppression of all the academies of 
Paris and the provinces. On this 
M. Bouillier ( * L'Institut et les Aca- 
demies,' p. 95) remarks : " Bientot 
il est vrai, les academies devaient 
renattre apres la chute de la 

It was of immense importance to the cause of science 
that in many of the discussions of that assembly a 
marked preference was shown for the scientific side of 
instruction. In this matter, as in many others, the suc- 
cessful constructive efforts of the Kevolutionary Govern- 
ments came from the side of those brought up in the 

Montagne et du Comity de salut 
public. Nous n'ignorons pas que 
c'est encore la Convention qui, prise 
d'un tardif remords, la veille seule- 
ment du jour oii elle devait faire 
place a un autre gouvernementmoins 
desputique et moins cruel, decreta 
I'organisation de I'lnstitut. Mais 
la Convention du 3 brumaire an 
iv. n'etait plus celle de 1793 ; c'dtait 
en rdalite une autre Convention, 
^purde, ddcim^e, renouvelee, animee 
d'un tout autre esprit," &c., &c. 
The idea of a national Institute for 
the advancement of letters, science. 
?ind arts was a very early one (see 
* Rapport de Talleyrand Perigord,' 
September 1791, Hippeau, p. 102). 
The explanation how the same 
Government which was labouring at 
the problem of a national instruc- 
tion, crowned by the higher teaching 
and research of an Institute, could 
begin by closing the existing acad- 
emies and universities, lies in this, 
that the aim was to make education 
general and learning popular, not 
merely fashionable, as it had been. 
See, for instance, what Ducos said 
on the 18th December 1792 : "Les 
moeurs d'un peuple corrompu ne 
se r^generent point par de legers 
adoucissements, mais par de vigour- 
-euses et brusques institutions. II 
faut opter ouvertement entre I'^du- 
cation domestique et la liberty ; car 
■citoyens, tant que par une instruc- 
tion commune vous n'aurez pas 
rapproche le pauvre du riche, le 
faible du puissant ; tant que, pour 
me servir des expressions de Plu- 
tarque, vous n'aurez pas achemine h, 

une meme trace, et mould sur une 
meme forme de vertu tous les 
enfants de la patrie, c'est en vain 
que vos lois proclameront la sainte 
egalite, la Republique sera toujours 
divisde en deux classes : les citoyens 
et les messieurs" (Hippeau, 2® 
serie, p. 21). It was because the 
academies and colleges supported 
"les messieurs" that they were 
suppressed. In the end education 
must always begin from above, and 
before the people can be taught 
you must form their teachers. See 
Lakanal's Report on the Ecoles nor- 
males, Hippeau, vol. i. p. 408. The 
academies and colleges of the eigh- 
teenth century were closed in order 
to make room for that uniform 
system of public instruction de- 
scribed by Talleyrand and Condor- 
cet, but not without a frequently 
expressed admiration for the work 
which they had done. See the de- 
fence of the academies by Condor- 
cet (Hippeau, loc. cit., vol. i. p. 272), 
and the tribute to the *' College de 
France," by Gilbert Romme (ibid., 
vol. i. p. 308). The arguments for 
radical change are summed up by 
that speaker as follows : * ' L'exist- 
ence de ces corps privildgids blesse 
tous nos principes rep"blicains, 
attaque I'dgalitd et la liberty de 
penser et nuit aux progres des 
arts. Mais si leur organisation est 
vicieuse, les Elements en sont bons, 
et nous serviront utilement dans 
I'organisation nouvelle de I'instruc- 
tion publique que vous allez dd- 
crdter " (p. 309). 






school of Voltaire and the Encyclopsedists, whilst the 
work of destruction had been performed by the followers 
of Kousseau. No one has expressed himself on the value 
of scientific study and knowledge in a clearer or more 
far-seeing manner than Condorcet. In his ' Eeport and 
Project of a Decree on the General Organisation of Public 
Instruction,' which he presented to the National Assembly 
in the name of the Committee of Public Instruction, 
he says : ^ " Many motives have brought about the kind 
of preference which is accorded to the mathematical and 
physical sciences. Firstly, for men who do not devote 
themselves to long meditations, who do not fathom any 
kind of knowledge — even the elementary study of these 
sciences is the surest means of developing their intel- 
lectual faculties, of teaching them to reason rightly and 
to analyse their ideas.^ ... It is because in the natural 
sciences the ideas are more simple, more rigorously cir- 
cumscribed, it is because their language is more perfect, 
&c., &c. . . . These sciences offer a remedy for prejudice, 
for smallness of mind — a remedy, if not more certain, 
at least more universal, than philosophy itself.^ . . . Those 

^ It was presented on the 20th 
and 21st April 1792. See Hippeau, 
le serie, pp. 185-288. It was 
printed by order of the Convention, 
Paris, Imprimerie nationale, 1793. 

•J Ibid., p. 203. 

3 Ibid., p. 204. It is interesting 
to see how in all these reports the 
exact sciences are placed in the fore- 
ground. See, for instance, what 
Gilbert Romme says of the teaching 
of the proposed instituts : " Les 
sciences mathematiques et phys- 
iques, morales et politique?, I'agri- 
culture et les arts mecaniques, la 
litterature et les beaux-arts, com- 

poseront I'enseignement des insti- 
tuts ou Ton pourra suivre, dans 
leurs Elements, I'dchelle entiere des 
connaissances humaines" (vol. i. p. 
322). " Les lycees seront I'^cole des 
gens instruits ; ils embrasseront les 
sciences, les arts et les lettres dans 
toute leur etendue." One is forcibly 
reminded that the most perfect 
realisation of this arrangement of 
studies is to be found a century 
later in the provincial science col- 
leges of this country. The prefer- 
ence, however, is now given to 
science mainly for ultilitarian rea- 
sons : the difference is shown by 

who follow their course, see the coming of an epoch 
when the practical usefulness of their application will 
reach greater dimensions than were ever hoped for, when 
the progress of the physical sciences must produce a 
fortunate revolution in the arts. And lastly, we have 
yielded to the general tendency of men's minds, which 
in Europe seem to incline towards these sciences with 
an ever-increasing ardour. . . . Literature has its limits, 
the sciences of observation and calculation have none. 
Below a certain degree of talent, the taste for literary 
occupations produces either ridiculous pride or a mean 
jealousy towards such talents as one cannot attain. In 
the sciences, on the contrary, it is not with the opinion 
of men but with nature that we have to engage in a 
contest, the triumph of which is nearly always certain, 
where every victory predicts a new one." ^ 

" It is," says Lakanal, in his report on the " ficoles cen- 
trales," 16th December 1794, "of great importance for 
the nation to assure itself that the mathematical sciences 
are cultivated and deepened, for they give the habit 
of accuracy: without them astronomy and navigation 
have no guide; architecture, both civil and naval, has. 
no rule ; the sciences of artillery and of fortification have- 
no foundation." ^ Gradually, under the pressure of exter- 


the importance then attached to 
mathematics as a training of the 
intellect in precise thinking; now- 
adays it is the mechanical side that 
is favoured, and this is only too 
often destructive of the truly scien- 
tific and exact spirit. 

^ Hippeau, loc. cit., p. 258. Cf. 
p. 261 : '• Hatons - nous . . . de 
porter dans les sciences morales la 

philosophic et la methode des scien- 
ces physiques" (Condorcet). 

- Hippeau, vol. i. p. 432. It is 
interesting to see how the study and 
teaching of the sciences in course of 
the second half of the last century 
in France undergo a development. 
The literary interest predominates 
in Fontenelle. Buffou and Voltaire^ 
add to it the philosophical and 





, 20. 

Ecole nor- 
male. Ecole 

nal events, the exigencies of war and the defence of the 
country gain the upper hand, and a central establishment 
is founded to cultivate and teach the sciences and arts, 
" upon which depend the defence of the Eepublic by land 
and sea." ^ Few of the higher and philanthropic aims of 
the great educational leaders of the early years of the 
Kevolution— of Mirabeau, of Talleyrand, of Condorcet— 
were realised; little was done for primary education; 
but science can boast of having been worthily represented 
and supported in the two great schools which still bear 
their original designation, and which can show a record 
of celebrated names and magnificent work superior prob- 
ably to that of any other similar institution in Europe. 
They are the " ficole normale superieure " and the 
" £cole centrale des Travaux publics," better known by 
the title " ficole polytechnique." ^ The founders of this 

philanthropic, the Encyclopsedists 
and Condorcet the educational ; the 
events of the Revolution and the 
discussions in the Assemblies bring 
out more and more the instructive, 
the utilitarian, and the economical 
aspects. The only creations which 
resulted were those in which the 
latter aims were predominant. 

1 Lakanal, see Hippeau, vol. i. 

p. 447. 

2 To these two great schools must 
be added as a third the "Museum 
d'Histoire naturelle," "le plus mag- 
nifique ^tablissement que les scien- 
ces aient possede" (Cuvier, "^loge 
de Fourcroy," part ii. of the ' Eloges 
historiques,' p. 44, Strasbourg, 1819). 
The foundation of the " Ecole cen- 
trale des Travaux publics " was pro- 
posed by Bar^re on the 11th March 
1794, and definitely organised on 
the report of Fourcroy (Hippeau, 
vol. i. p. 446) by a decree of 7th ven- 
d^miaire, an iv. (name changed to 

Ecole polytechnique, 15th fructidor). 
The opening of the courses was an- 
nounced for the 10th frimaire fol- 
lowing (Hippeau, vol. ii. pp. 139, 174, 
175). The foundation of the " Ecoles 
normales " was proposed by Barere 
(13th prairial, an ii. ), and decreed on 
a report of Lakanal (Hippeau, vol. i. 
p. 423) on the 9th brumaire, an iii. 
(30th October 1794) (ibid., vol. ii. p. 
179). The courses opened on the 1st 
pluviose. The work of the school 
was distributed as follows : Mathe- 
matics, I^agrange and Laplace; 
physics, Haiiy; descriptive geome- 
try, Monge ; natural history, Dau- 
benton ; chemistry, BerthoUet ; agri- 
culture, Thouin ; geography, Buache 
and Mentelle ; histoiy, Volney ; 
morals, Bernardin de St Pierre. 
(Hippeau, vol. ii. p. 180, where also 
will be found extracts from the 
' Moniteur ' of the 9th pluviose on 
the opening addresses. ) The oldest 
pupil was Bougainville, the g;reat 

magnificent institution recognised " that, in spite of the 
diversity of applications, mathematics and physics are 
the indispensable basis of the studies in view." ^ Though 
the first period of the life of the £cole normale only 
counted four months,^ we are indebted to it for the 

traveller. The Ecole polytechnique 
received an allocation of £12,000, 
and had 400 pupils to start with. 
On the 20th frimaire, an iii., the 
Convention, on a report of Thibau- 
deau, voted the necessary expenses 
for the enlargement of the Museum 
d'Histoire naturelle (Hippeau, vol. 
ii. p. 196),— viz., nearly £8000 for 
expenses, and £200 for each of the 
professors. The Museum had been 
originally destined for the culture 
of medicinal plants. Tournefort had 
given a great impetus to botanical, 
and Buffon, with Daubenton, to 
zoological studies. The Convention 
added several to the courses regu- 
larly held there on natural history, 
botany, mineralogy, and general 
chemistry. " Ces cours," says Thi- 
baudeau, "fournissent 500 le9ons 
par an, offrent I'ensemble le plus 
vaste et le plus complet d'enseigne- 
ment sur toutes les branches d'his- 
toire naturelle dont le plus gi-and 
norabre manquaient totalement k la 
France et dont quelques-unes man- 
quent encore k 1 'Europe, I'applica- 
tion immediate de toutes les sciences 
naturelles au commerce et aux arts." 
Of other scientific and teaching 
institutions I must mention the 
** Bureau des Longitudes." This 
was organised by the Convention 
on a discourse by Gr^goire, 7 th 
messidor, an iii. (24th June 1795), 
in which he refers to the British 
Board of Longitude and the superi- 
ority of the British navy (Hippeau, 
vol. ii. p. 219). The appointments to 
this bureau were the g^ometres La- 
grange and Laplace, the astronomcs 
Lalande, Cassini, Mechain, De- 


lambre, one of whom had to deliver 
a course of astronomy, the travellers 
Borda, Bougainville, the g4ographe 
Buache, and the artist Carocher. 
It had charge of the observatory, 
which had already been reorganised 
by a decree promoted by Lakanal on 
the 31st August 1793 (Hippeau, vol. 
ii. p. 76), and published in the * Con- 
naissance des Temps.' There were, 
besides, several military schools and 
the medical schools, not to mention 
other foundations less connected 
with our subject but equally im- 
portant, such as the School of 
Oriental Languages, established in 
the Bibliotheque nationale (ger- 
minal,,an iii., Hippeau, vol. ii. p. 215) ; 
the Ecoles de Sant^, established 
14th frimaire, an iii., on a report of 
Fourcroy, in Paris, Strasbourg, and 
Montpellier (Hippeau, vol. ii. p. 194). 

^ Ibid., vol. i. p. 450. 

^ The Ecole normale was closed 
on the 30th flordal, an iii., on a 
decree of the Convention dated 
the 7 th of that month. Dan ton 
explained that the school had not 
taken the line which the Conven- 
tion had marked out — the courses 
in general having offered a direct 
teaching of the sciences rather 
than an exposition of the methods 
which are to be adopted in teaching 
(Hippeau, vol. ii. p. 215). It also 
seems that the eminent teachers of 
this institution had few pupils sufl&- 
ciently, prepared to follow them. 
The Ecole normale was reopened 
in the year 1808 under the Empire, 
by the same decree of 17 th March 
which organised the University of 




21. foundation of a new branch of science — the ' Descriptive 

^Descriptive Geomctry ' of Monge, which was given to the world 

"'"'^ '^* through shorthand notes ^ from his lectures delivered in 

that institution. They form the beginning of the new 

science, since developed by Poncelet, Steiner, and others, 

and known under the name of " projective geometry." ^ 

Next to mathematics with its analytical and graphical 
application to physics and the arts, the subject most culti- 
vated in these higher educational establishments of Paris 
at the end of the last century was the new science of 
chemistry. With some justice this science has been termed 
a French science,^ not so much because even at that time 


Science of 

1 See the account of the origin of 
this branch of mathematics in Bris- 
son's edition of the ' Geometric de- 
scriptive,' Paris, 1847. In the pro- 
gramme prefixed to the treatise the 
three aspects of the new school — 
the national, the practical, and the 
educational — are well set forth : 
" Pour tirer la nation francaise de 
la d^pendance oh elle a ^t^ jusqu'h 
present de I'industrie etrang^re, il 
faut premi^rement dinger Teduca- 
tion nationale vers la connaissance 
des objets qui exigent de I'exacti- 
tude. ... II faut, en second lieu, 
rendre populairelaconnaissance d'un 
grand nombre de phenomenes natu- 
rels. ... La geometric descriptive 
est un moyen de rechercher la ver- 
ity ; elle offre des exemples perpe- 
tuels du passage du connu h, I'incon- 
nu ; et parcequ'elle est tou jours ap- 
pliquee a des objets susceptibles de 
la plus grande evidence, il est n^ces- 
saire de la faire entrer dans le plan 
d'une Education nationale." Monge 
generalised and placed on a scien- 
tific basis the methods used pre- 
viously by carpenters and stone- 
cutters, and partially dealt with 
geometrically by Courcier, Derand, 
Mathurin, Jousse, and Frezier. See 

Montucla, ' Histoire des Mathema- 
tiques,' vol. iii. p. 15. 

'^ Monge taught also at the Ecole 
polytechnique from the beginning. 
See the remarks of Chasles (* Rap- 
port sur les Progr^s de la Geo- 
metric,' Paris, 1870, p. 2): "L'en- 
seignement theorique et profond 
qui a ^t^ la base de la premiere et 
judicieuse organisation de ce grand 
etablissement ^tait eminemment 
favorable aux progrfes de la science, 
en meme temps qu'il preparait seri- 
eusement les eleves h I'entree dans 
les ecoles d'application. " The au- 
thor then refers with regret to the 
less scientific tone which had crept 
into the studies of that great school 
in the course of this century. See 

also p. 379. 
3 A. WurtzCHistoire des Doctrines 

chimiques,' Paris, 1868, p. 1) : "La 
chimie est une science francaise ; 
elle fut constitu^ par Lavoisier." 
Cf. Dumas (* Lecons sur la Philoso- 
phic chimique,' Paris, 1837, p. 137). 
Buckle ('History of Civilisation,' &c., 
3 vols., vol. ii. p. 366, London, 1866) 
says : **That we owe to France the 
existence of chemistry as a science 
will be admitted by every one who 
uses the word science in the sense 


chemistry was not indebted to illustrious foreigners ^ for 
some of its most important discoveries, as because the 
modern scientific spirit of accurate measurement first took 
hold of chemical phenomena on a large scale in the many 
important investigations which bear the name of Lavoi- 
sier and his followers, through whom the great reform of 
modern chemical knowledge and research was permanently 
established. It has been significantly pointed out ^ that it 
was the union of mathematical with empirical knowledge 
which, through men like Laplace, Meusnier, Monge, first 

in which alone it ought to be un- 
derstood, &c. . . . Until Lavoisier 
entered the field there were no gen- 
eralisations wide enough to entitle 
chemistry to be called a science." 
The correctness of this view is fully 
and impartially examined by Her- 
mann Kopp (' Die Entwickelung der 
Chemie in der neueren Zeit,' Miin- 
chen, 1873, p. 89, &c.) He fully 
upholds the claims of Lavoisier to 
be called the father of modern 
cheniistry (p. 145). See also what 
Liebig says. 

1 These were mainly. Black (dis- 
covered carbonic acid, called fixed 
air, in 17.54), Cavendish (discovered 
hydrogen or inflammable air in 
1767), and Priestley, who between 
1771 and 1774 discovered oxy- 
gen (dephlogisticated air), nitrogen 
(phlogisticated air), and several of 
its compounds, among them am- 
monia (alkaline air). Of Priestley 
it is said by Cuvier that he may 
well be considered as one of the 
fathers of modern chemistrj^, " mais 
c'est un p^re qui ne vpulut jamais 
reconnaitre sa fille " (' Eloges,' vol. i. 
p. 208). Elsewhere (* Rapport his- 
torique sur les Progr^s des Sciences 
naturelles,' Paris, 1810, p. 90) Cu- 
vier dates the revolution in chem- 
istry from the introduction of the 
mathematical spirit: "II en est 

une cause encore plus essentielle h 
laquelle meme on doit h proprement 
parler, et cette thdorie nouvelle, et 
les decouvertes qui I'ont fait naitre. 
. .^ . C'est I'esprit mathematique 
qui s'est introduit dans la science 
et la rigoureuse precision qu'on a 
portee dans I'examen de toutes ses 
operations. . . . C'est dans le 
Traits ^lementaire de Lavoisier que 
I'Europe vit pour la premiere fois 
avec etonnement le syst^me entier 
de la nouvelle chimie," &c. 

2 Kopp, loc. cit., p. 202: "In- 
deed, if we look at those who first 
worked together with Lavoisier or 
in his spirit, we shall find such as 
had devoted themselves principally 
to mathematics or mathematical 
physics, men like Laplace, Meus- 
nier, Monge. Among chemists La- 
voisier stood for a long time almost 
alone in his opinions." This view 
is also taken by Cuvier ('Rapport,' 
p. 91): **Les nouveaux chimistes 
frangais . . . ont eu h, se louer du 
concours de quelques-uns de nos 
g^ometres les plus distingues," &c.; 
and he attributes the next great 
step in chemical science to a similar 
introduction of a "rigueur toute 
mathematique" ('Rapport sur la 
Chimie lu k la Seance des 4 Acad.,' 
23rd April 1826). 





brought about the general recognition of Lavoisier's ideas ; 
whereas the more exclusive representatives of chemistry, 
such as BerthoUet and Guyton, held aloof for some con- 
siderable time. In the earlier syllabus of the Ecole 
polytechnique, chemistry was brought into a similar 
proximity with the mathematical branches. And Ber- 
thoUet's ' Statique chimique ' denotes by its title alone 
^the mathematical spirit in which the work was conceived. 
• 23 About that time also two new sciences were, if not 

IZ^"^" invented, at least set on a firm basis, by which the use 
"''""• of mathematics was very largely extended, and by which 
great realms of interesting facts were made accessible to 
accurate measurements and exact reasoning. Both these 
sciences can be claimed by France a^ almost exclusively 
her own creations. They are the science of crystallo- 
graphy and the great theory of probabilities. The former 
was the work of the Abbe Haliy ; the latter formed, next 
to the mechanics of the heavens, the main original con- 
tribution by which Laplace has perpetuated his name in 
the history of science. (The theory of the Abbe Haiiy, 
who first taught how crystals are built up from small 
particles of definite and regular geometrical forms, such as 
cubes, pyramids, &c., came to the aid of the mineralogists, 
who before him had vainly groped in the dark, searching 
for some method by which order and system could be 
introduced into the lifeless forms of nature as by the 
methods of Linn^us and Jussieu it had been introduced 
into the world of plants and animals. Before Hauy, 
the doctrines of mineralogy had been either attached to 
geology— especially in the celebrated school of Werner, 
or latterly, after the great developments in chemistry had 



set in, to chemistry — especially by Bergmann.^) Haliy 
established the science of minerals on an independent 
foundation by studying and systematising the forms of 
their crystallisation ; and he brought the science of min- 
eralogy from Sweden and Germany into France, and gave 
it an independent position. Thus it came to form a con- 
necting-link between the mathematical — i.e., the measur- 
ing and calculating — and the purely descriptive sciences. 
"Mineralogy, though it is that part of natural science 
which deals with the least complicated objects, is never- 
theless also that which lends itself least to a rational 
classification. The first observers named the minerals 
vaguely according to their external appearances and their 
use. It was not until the middle of the eighteenth 
century that it was attempted to subject them to those 
methods which had done service to geology and botany : 
the hope existed of establishing among them genera and 

^ See an account of the work of 
the chemical school, to which Cron- 
sted (the inventor of the blow-pipe), 
Bergmann, Kirwan, and Klaproth 
belonged, in Cuvier's ' Rapport ' (p. 
163). Also his " Eloge de Haiiy " 
('Eloges histor.,' vol. iii. p. 143, &c.) 
The beginnings of geometrical crys- 
tallography seem to go back to Lin- 
naeus ; but his view was discouraged 
in France by Buffon, who disliked 
Linnseus's writings. Whewell, who 
was himself an authority on crys- 
tallography, thinks Rom^ de I'lsle, 
who was not an Academician, had 
only scant justice done to him by 
Haiiy and his friends ('Hist, of 
the Induct. Sciences,' 3rd ed., vol. 
iii. p. 176). More recent writers, 
such as Kobell (' Geschichte der 
Mineralogie,' Miinchen, 1864, p. 73, 
&c.) and Nicol (article "Crystal- 

lography," ' Ency. Brit.'), have done 
him justice. The 'Grande Ency- 
clopedic ' thus summarises the work 
of Rom^ de I'lsle : "II mesura 
mecaniquement [viz., with Caran- 
geot's goniometer] les angles et 
etablit que ces angles ont tou jours 
une valeur constante dans une 
meme espece mineralogique." That 
of Haiiy is summarised in the two 
laws : "1°, Tous les elements sem- 
blables d'un cristal sont toujours 
semblablement et simultandment 
modifies (loi de sym^trie) ; 2°, toute 
facette modifiante intercepte sur 
les aretes de la figure primitive 
des longueurs proportionelles h. des 
multiples simples de la longueur 
de ces aretes (loi de derivation) " 
(Berthelot in 'Grande Ency clop.,* 
vol. xiii. p. 397). 





species, as among organised beings, and it was forgot- 
ten that in mineralogy the principle is absent which 
had given birth to the idea of species — viz., that of 
generation. The principle of individuality, such as it is 
conceived in the organic world — viz,, the unity of action 
of different organs which co-operate in the preservation of 
the same life — can scarcely be admitted in mineralogy."^ 
The Abb^ Hauy, by founding the science of minerals 
on their regular forms of crystallisation, made mineralogy 
"as precise and methodical as astronomy; in fact, we 
can say in one word that he was to Werner^ and Kome 
de risle, his predecessors, what Newton had been to 
Kepler and Copernicus."^ 

From that well-defined province of science which deals 
p?Siiity. in a precise and strict manner with the simple numerical 
relations which seem to underlie all forms of movement 
in nature, be they on a stupendous or on a minute scale 

Theory of 

^ Cuvier, " Eloge de Haliy" in 
* Eloges historiques,' vol. iii. p. 155. 

'^ The character of Werner (1750- 
1815) is nowhere better , painted 
than by Cuvier in his " Eloge de 
Werner" {loc. cit., vol. ii. p. 303, &c.) 
" II commence I'epoque la plus re- 
marquable de la science de la terre, 
et meme Ton pent dire qu'h. lui 
seul il la remplit. ... II s'est 
form^ des academies enti^res, qui 
ont pris son nom" (for instance, 
the Edinburgh Wernerian Society, 
founded by Jameson, 1808-1859), 
"comme si elles eussent voulu in- 
voquer son gdnie et s'en faire un 
patron d'une espece auparavant in- 
connue. Qui ne croirait, h. entendre 
parler de succ^s si peu ordinaires, 
que ce fut quelqu'un de ces hommes 
ardens a propager leur doctrine, 
qui par des ouvrages nombieux et 

eloquens, ont subjugu^ leurs con- 
temporains, ou qui se sont procure 
des partisans par I'ascendant d'une 
grande richesse ou d'une position 
elev^e dans I'ordre social ? Rien de 
tout cela : confine dans une petite 
ville de Saxe, sans autorite dans 
son pays, il n'avait aucune influence 
sur la fortune de ses disciples ; il 
n'entretenait point de liaisons avec 
des personues en place : d'un nat- 
urel singuli^rement timide, hesitant 
tou jours h ecrire, b, peine subsiste- 
t-il de lui quelques feuilles d'im- 
pression. . . . C'est ainsi qu'en 
peu d'ann^es la petite ^cole de 
Freyberg, destinee seulement, dans 
le principe, h, former quelques 
mineurs pour la Saxe, renouvela 
le spectacle des premieres univer- 
sit^s du moyen S-ge," &c., &c. 
^ Cuvier, ibid., p. 163. 

— i.e., from the province of mechanics and astronomy — 
two different roads lead into those extensive domains in 
which, not simplicity and regularity, but endless variety 
and complication, seem to be the order and the rule of 
Life. Even a century ago the contrast must have been 
striking between the 'Principia ' of Newton and the ' Ex- 
position du Systeme du Monde ' of Laplace on the one 
side, and the great array of volumes of Linnaeus, Buffon, 
Jussieu, Cuvier, and Lacepede on the other ; though these 
after all embraced only a small portion of the living forms 
of nature which they attempted to classify or to describe.'^ 
I have pointed out how the new and especially the 
French methods of chemistry and crystallography con- 
quered a large portion of intermediate ground, subjected 
many tangled phenomena to exact treatment, and pushed 
the mathematical method far into the dominion of natural 
history. It is that other history, not natural, but human 
and often unnatural, which presents the opposite extreme 
of the great panorama of world-life. It is significant 
that almost at the same time that mathematical reason- 
ing found its way into natural history, conquering an ex- 
tensive province of its vast territory, an entirely different 
method was invented with the aim of dealing in a still 
more vigorous manner with the phenomena of human 
life and society. This was the science of statistics, and 

^ Cuvier gives some figures as to 
the increase of the known species 
•during his own lifetime. Lacepede 
had described about 1200 or 1300 
-distinct species of fishes ; but when 
Cuvier pronounced his Eloge in 
1826, the Cabinet du Roi contained 
already more than 6000 species 
((* Eloges historiques,' vol. iii. p. 317). 

Linnaeus had counted in 1778 about 
8000 species of plants. Cuvier in 
1824 estimates the number as 
50,000 or more (see 'Eloges,' vol. iiL 
p. 469, &c., where he also gives some 
idea of the numbers of known 
species in the different classes of 





connected with it the doctrine of averages and the mathe- 
matical theory of probabilities.^ The same great mind 

* The beginnings of the science 
and theory of probabilities are not 
subject to controversy, as were 
those of the infinitesimal calculus. 
Pascal and Fermat about the middle 
of the seventeenth century entered 
into a correspondence relative to a 
question in a game of chance, pro- 
pounded by the Chevalier de Mer^, 
a noted gambler. They agreed in 
their answer, but could not con- 
vince their friend, who moreover 
made this the occasion of denounc- 
ing the results of science and arith- 
metic. But this comparatively in- 
significant problem — so difierent 
from the great cosmical problems 
which led to the invention of the 
infinitesimal calculus about the 
same time — was the origin of a 
series of investigations and discus- 
sions in which the greatest mathe- 
maticians, such as Huygens, James 
and Daniel Bernoulli, De Moivre, 
D'Alembert, and Condorcet joined. 
Most of them did not escape the 
errors and misstatements which 
creep in an insidious manner into 
the discussion and vitiate the conclu- 
sions. In fact, the science advanced 
through the influence of those who 
depreciated it like D'Alembert, and 
those who exaggerated its import- 
ance like Condorcet. At length, 
under the hands of Laplace, who 
defined it as common -sense put into 
figures and attributed to it a high 
educational value, it assumed a state 
wellnigh approaching to that per- 
fection which Euclid gave to geo- 
metry and Aristotle to logic. Since 
the publication of Laplace's cele- 
brated ' Theorie analy tique des Pro- 
babilit^s' (Paris, 1812) writers on 
the subject have found ample oc- 
cupation in commenting on the 
theorems or recasting the proofs 
given in that work, which holds a 
similar position to that occupied in 

another department of mathematics 
by the 'Disquisitiones Arithmetical ' 
of Gauss (1801). Up to the pres- 
ent day there exist differences of 
opinion as to the value of the 
science, the two opposite views be- 
ing represented in this country by 
Mill ('Logic,' 5th ed., vol. ii. p. 62) 
and Jevons (' Principles of Science,' 
vol. i. ), the latter summing up his 
opinion as follows : " In spite of its 
immense difficulties of application, 
and the aspersions which have been 
mistakenly cast upon it, the theory 
of probabilities is the noblest, as it 
will in course of time prove perhaps 
the most fruitful, branch of mathe- 
matical science. It is the very^ 
guide of life, and hardly can we 
take a step or make a decision of i 
any kind without correctly or in- / 
correctly making an estimation oiJ 
probability" (Ist ed., p. 248). A 
similar opinion seems to have been 
held by James Clerk Maxwell (see 
Life by Campbell and Garnett, p. 
143), who called the calculus of 
probabilities " Mathematics for 
practical men." In this country 
A. de Morgan and Todhunter, the 
former in a popular essay in the 
'Cabinet Cyclopaedia' and in a 
profound treatise in the ' Encyclo- 
paedia Metropolitana,' the latter in 
his well - known History (London 
and Cambridge, 1865), have done 
a great deal to make this subject 
better understood. The applica- 
tions of the theory have gradually 
increased through numerous mor- 
tality and insurance calculations; 
as also in the estimations of error 
in astronomical and physical ob- 
servations, where the well-known 
method of least squares (first em- 
ployed by Gauss in 1795, see Gauss, 
Werke, vol. vii. p. 242 ; first pub- 
lished by Legendre in 1806, and then 
proved by I^place in his * Theorie,* 

which elaborated the principles of Newton into a system 
of the universe, and attacked the intricate mathematical 
problem which this system presented, gave to the world 
likewise the first complete treatise on that calculus which 
comes into play if we eliminate from the apparently most 
arbitrary region of phenomena, that of human life and 
history, all regard for final or efficient causes, for provi- 
dential design and freewill, for human error, human malice 
and benevolence — in fact, all notice of that element which 
from another and equally important point of view forms 
the subject of greatest interest — the inner life of the in- 
dividual. It was proposed, and it has since been carried 
out, to look upon human beings and human events not as 
things possessed of an inner world of thought and freewill, 
but as lifeless units, more uniform and regular than the 
balls thrown into the urn at an election, or the counters 
in a game of chance. By overstepping with one bound 
the great field of human activity, full of so much con- 
fusion and so much interest, it was proposed to investi- 
gate what knowledge would result from a purely mathe- 
matical inspection, in which human beings figured merely 
as units and symbols.^ This attempt, which has since 

&c., 1812) is now extensively em- 
ployed. Of this branch of mathe- 
matics Bertrand says : " Les plus 
grands g^ometres ont dcrit sur le 
calcul des probabilites ; presque 
tous ont commis des erreurs : la 
cause en est, le plus sou vent, au 
ddsir d'appliquer des principes h, 
des problemes qui par leur nature 
^chappent k la science." In the 
hands of Clerk Maxwell the cal- 
culus has acquired an additional 
interest and importance through 
the distinction which he made be- 
tween what he termed the "histori- 

cal" and the "statistical method'* 
of treating phenomena, and the 
application of the latter to the 
kinetic theory of gases (see Life,, 
pp. 438, 562). This subject will 
occupy our attention in a special 

1 The beginnings of the science of 
statistics belong likewise to the age 
that produced the higher mathema- 
tics. More extensive "countings'* 
seem to have been contemporaneous 
with more refined calculations. Her- 
mann Conring, professor at Helm- 
stadt, a friend of Leibniz (see Leib- 



led to such interesting results, and which has furnished 
almost all the knowledge upon which a judicious regula- 
tion and government of society depends, was the work of 
Laplace, and was produced in an age and in a nation 
which seemed to have set at naught all ideas of order and 
method in human affairs, which defied all authority and 
all tradition, and trusted its fate to the most radical 
revolution which civilised society ever witnessed.^ 

It is curious to read the criticism which the first 
Napoleon, that wayward child of the Kevolution, passed 
on the author of the mechanics of the heavens and the 
theory of probability. Laplace, like so many other men 
of science, had been called by the Emperor to assist in 
the labours of administration, but, according to his judg- 
ment, proved himself a poor administrator, being unable 

iiiz's ' Philosophische Schriften,' ed. 
Gerhardt, vol. i. p. 155), lectured 
About 1660 on subjects now com- 
prised under the term " Statistics," 
And about the same time John Graunt 
^f London published ' Natural and 
Political Annotations made upon 
the Bills of Mortality ' (1666). Sir 
William Petty, one of the founders 
.of the Royal Society, published in 
1683 'Five Essays in Political 
Arithmetick.' The newly discov- 
ered calculus of probabilities in- 
duced mathematicians to take an in- 
terest in the subject, and to urge the 
^desirability of gaining data for their 
calculations. Many of these turned 
upon questions of mortality and 
the ravages of diseases, such as the 
smallpox. But though undoubt- 
.edly the fact that during the 
French Revolution mathematicians 
ior the first time had a great in- 
fluence in administrative and gov- 
ernmental matters contributed 
enormously to the introduction of 
-Statistical methods, the great epoch 

in this science is allied with the 
name of the Belgian Quetelet 
(1796-1874), of whom more later 

1 Cantor ( ' Historische Notizen 
liber die Wahrscheinlichkeitsrech- 
nung,' Halle, 1874, p. 6) says: 
"The tendency of thought which 
prepared the Revolution, and which 
is marked by an unsparing and de- 
structive criticism of the conditions 
of society in state and family, could 
not dispense with an instrument 
which, more than any other, enables 
one to subject to general views the 
most different factors of civilisation. 
It belonged to the favourite ideas of 
that age, that the calculus of proba- 
bilities should be among the most 
important subjects of public in- 
struction ; for it was said to be the 
calculus of common-sense, through 
which alone the influence of hope, 
fear, and emotion on our judgment 
could be destroyed, and prejudice 
and superstition removed from the 
decisions of social life. " 



to grasp practical issues, and always descending into in- 
finitesimals. It is hardly to be doubted now, after the 
lapse of a century, that the infinitesimals of Laplace play 
a more important part in problems of administration and 
government than the ideas of Napoleon. Laplace, un- 
like some other great scientific thinkers, attached great 
value to a popular exposition of the principles of his dis- 
coveries. Descartes required a Fontenelle and Newton a 
Voltaire to make their ideas accessible and useful to the 
mass of students. Laplace was his own Fontenelle and 
Yoltaire. " Few works," says Sir John Herschel, " have 
been more extensively read, or more generally appreciated, 
than Laplace's ' Essai philosophique sur les Probabilites,' 
and that on the ' Systeme du Monde ' by the same author. 
It is not, perhaps, too much to say that were all the 
literature of Europe to perish, these two essays excepted, 
they would suffice to convey to the latest posterity an 
impression of the intellectual greatness of the age which 
could produce them, surpassing that afforded by all the 
monuments antiquity has left us. Previous to the pub- 
lication of the ' Essai philosophique,' few, except professed 
mathematicians or persons conversant with assurances 
and similar commercial risks, possessed any knowledge of 
the principles of this calculus, or troubled themselves 
about its conclusions, regarding them as merely curious 
and perhaps not altogether harmless speculations. Thence- 
forward, however, apathy was speedily exchanged for a 
lively and increasing desire to know something of a system 
of reasoning which for the first time seemed to afford a 
handle for some kind of exact inquiry into matters no one 
had ever expected to see reduced to calculation, and bear- 





ing on the most important concerns of life. Men began 
to hear with surprise, not unmingled with some vague 
hope of ultimate benefit, that not only births, deaths, and 
marriages, but -the decisions of tribunals, the results of 
popular elections, the influence of punishments in check- 
ing crime, the comparative value of medical remedies and 
different modes of treatment of diseases, the probable 
limits of error in numerical results in every department 
of physical inquiry, the detection of causes, physical, 
social, and moral— nay, even the weight of evidence and 
the validity of logical argument — might come to be sur- 
veyed with that lynx-eyed scrutiny of a dispassionate 
analysis, which, if not at once leading to the discovery of 
positive truth, would at least secure the detection and 
proscription of many mischievous and besetting fallacies." 
Both ways of approaching the intricate phenomena of 
nature and history, that of mechanics dealing with the 
general laws of motion and of lifeless masses, and that 
of statistics dealing with the arithmetical properties of 
large numbers of units, leave out of consideration that 
hidden and mysterious phenomenon to which alone is 
attached, if not order and method, yet certainly all 
that commands interest in the created world : the factor 
2g^ of life— the existence of individuality. The view which 
^S^^'liis Laplace took of the universe or of human affairs is an 
dlsregl^^.. attempt to see how far science and reasoning can go 
dfieonr' ^y^iiq disregarding the principle of individuality.^ The 

dividuality. "" '^ o o j- 

1 See Clerk Maxwell on * Science 
and Freewill' (Life by Campbell 
and Gamett, p. 438) : ** Two kinds 
of knowledge, which we may call for 
convenience dynamical and statis- 
tical. The statistical method of 

investigating social questions has 
Laplace for its most scientific and 
Buckle for its most popular ex- 
pounder. Persons are grouped 
according to some characteristic, 
and the number of persons forming 

method has been most fruitful, and, far from being ex- 
hausted, promises undreamt of results in the future. It 
was probably more from the desire to keep his view 
clear and his method simple, than with any necessarily 
sceptical tendency, that when Laplace was questioned by 
Napoleon how it was that in the great volumes of the 
' Mecanique celeste ' the name of God did not appear, he 
replied, " Sire, je n'ai pas besoin de cette hypoth^se." 

But French science did not leave that great field of 27. 


research uncultivated, which is the very playground of f^^l^^^^ 
individual life. Its cultivation was the work of that i^*'scienc''e3 
other great representative of French science — the con- ° 
temporary of Laplace — Georges Cuvier.^ Linnaeus had 

the group is set down under that 
characteristic. This is the raw 
material from which the statist 
endeavours to deduce general theo- 
rems in sociology. Other students 
of human nature proceed on a dif- 
ferent plan. They observe indi- 
vidual men, ascertain their history, 
analyse their motives, and compare 
their expectation of what they will 
do with their actual conduct. This 
may be called the dynamical method 
of study as applied to man. How- 
ever imperfect the dynamical study 
of man may be in practice, it evi- 
dently is the only perfect method 
in principle, and its shortcomings 
arise from the limitation of our 
powers rather than from a faulty 
method of procedure. If we be- 
take ourselves to the statistical 
method, we do so confessing that 
we are unable to follow the details 
of each individual case, and expect- 
ing that the effects of widespread 
causes, though very different in each 
individual, will produce an average 
result on the whole nation, from a 
study of which we may estimate 
the character and propensities of 

an imaginary being called the Mean 

^ It is not necessary here to ex- 
plain the reasons which have in- 
duced me to confine myself mainly 
to the two great names of Laplace 
and Cuvier as the great repre- 
sentatives of the exact scientific 
spirit, as it first asserted its su- 
premacy in France, and from there 
gradually fought its way all over 
Europe. To me it seems that no- 
where has this modern scientific 
spirit been represented in greater 
completeness and greater purity. 
This is so much the more remark- 
able, as other influences and tempta- 
tions were not wanting in that age 
and country which might have in- 
terfered with the application of 
the purely scientific method. The 
scientific spirit is in danger of being 
contaminated by two interests which 
are essentially foreign to it : the 
one is the practical, the other the 
philosophical. Frequently they are 
united ; and when united their influ- 
ence on the progress of science has 
frequently been disastrous. In no 
department of knowledge has this 






begun the work of natural history by inventing a system 
of classification and a technical language or nomenclature. 
Buffon in his brilliant and elegant portraits had cast around 
it the charms of poetry and romance. Jussieu had im- 
ported botany from Sweden into France, and in the garden 
of Trianon had given a living model of the arrangement 
of plants; botanising had become popular through the 

psychological as a physical side, 
and a philanthropic as much as 
a scientitic interest. In respect of 
this it is well to note that the age 
and country which gave to Europe 
the great models of purely scientific 
research in Laplace and Cuvier was 
rich also in great thinkers who 
applied themselves in a philoso- 
phical spirit to the advancement of 
scientific and practical medicine, to 
the reform of hospitals, to the care 
of the insane, to the education of 
the deaf and dumb. The whole 
school of the ideologues, headed by 
Condorcet, Cabanis, and Destutt 
de Tracy, was closely allied with 
the medical profession. But how- 
ever important this side of French 
thought may have been, its in- 
fluence on the rest of Europe at 
that time cannot be compared 
with that of the purely scientific 
writings belonging to mathematics 
and natural science. Such names 
as Cabanis and Bichat belong to 
a different current of European 
thought, which I purposely separate 
from the exact or purely scientific. 
And this separation is justified his- 
torically by the fact that in the 
Academic des Sciences for a con- 
siderable time medical science was 
only meagrely represented, whilst 
philosophy during the period of the 
suppression of the Acaddmie des 
Sciences morales et politiques, from 
1803-1832, had no academic re- 
presentation at all. The great 
name of Bichat is not among the 
Academicians, and Cuvier himself 

union of the practical and philo- 
sophical spirit been more marked 
than in the medical sciences. Essen - 
tiallv interested as it is in the im- 
mediate application of scientific dis- 
coveries to the needs of suffering 
mankind, we witness in the course 
of the seventeenth and eighteenth 
centuries a one-sided alliance of the 
art of healing with chemistry (Sylvi- 
us, 1814-1672), with physics (Borelli, 
1608-1679), and with mechanics (Pit- 
cairn, 1652-1713), and the reaction 
of the animists (Stahl, 1660-1734, 
and Hoffmann, 1660-1742), and the 
vitalists (Bordeu, 1722-1776, and 
Barthez, 1734-1806). A large por- 
tion of the history of medicine (see 
Haeser, ' Geschichte der Medicin,' 
Jena, 1881, vol. ii., and Guardia, 
' Histoire de la Medecine,' Paris, 
1884) consists in the account of the 
opposition to premature generalisa- 
tions, adopted from other sciences, 
or still more dangerously from meta- 
physics. As examples of the meta- 
physical tendency we have the Scotch 
systems of CuUen and Brown, and 
the German "Philosophy of Nature." 
The reasons why philosophy has so 
frequently allied itself with medi- 
cine, thus preventing the purely 
scientific spirit from gaining ad- 
mission, are twofold. " Young 
men," says Cuvier, "adopt these 
theories with enthusiasm, because 
they seem to abridge their studies 
and to give a thread in an almost 
inextricable labyrinth" ('Rapport,' 
p. 383). The other reason is that 
the art of healing has as much a 

writings of Eousseau ; gardening and the study of plant- 
life had become a royal pastime, and a favourite recrea- 
tion for those oppressed with the troubles of the State 
or the sorrows of private life. Cuvier, while asking the 
reason why other portions of natural history had not 
shared the same attention, breaks out into the following 
eloquent words : " The study of animals presents diffi- 

explains the exclusive attitude of 
the Academy to the medical pro- 
fession in his Eloges of Halle, Cor- 
visart, and Pinel ('Eloges,' vol. iii. p. 
339, &c. ) See also Maury (p. 304) : 
" Les sciences physiques, chimiques 
et naturelles avaient pris une telle 
extension dans les travaux de 
I'Acaddmie, qu'h la fin du dix- 
huiti^me si^le, la medecine, qui 
n'y avait jamais ^te au reste bien 
largement representee, fut de plus 
en plus relegu^e h, I'arri^re plan ; 
ce n'etait plus que de loin en loin 
que les medecins, les chirurgiens de 
la Compagnie, . . . y pr^sentaient 
des observations sur des points 
medicaux. ... La medecine, qui, 
selon la juste observation de Cabanis, 
tend aux hypotheses par la nature 
meme du sujet auquelelles'applique, 
n'offrait point assez de Constance 
dans ses principes et d'^vidence 
dans ses demonstrations pour satis- 
faire des esprits qui se ddtachaient 
tons les jours davantage des vieilles 
speculations de I'dcole. C'est ce qui 
explique le peu de faveur qu'elle 
rencontrait h 1' Acad^mie." To what 
extent this rigid demarcation, ac- 
cording to which '* observations 
relatives aux dispositions morales 
et intellectuelles des individus 
n'entrent assurement dans les 
attributions d'aucune academie des 
sciences " (' Memoires de I'lnstitut,' 
vol. ix. p. 110), was beneficial to 
medical science is an important 
question. In the organisation of 
the Institute of the 3rd brumaire, an 
iv. (25th October 1795), there are 

awarded out of 60 members only 6 
to medicine and surgery combined, 
and in the " nouvelle organisation " 
of 3rd pluviose, an xi. (23rd January 
1803), there are 6 members out of 
63. This section is given as the last, 
even after " ^conomie rurale et art 
v^terinaire"(see Aucoc, 'L'Institut,* 
p. 3, &c. ) It is interesting to note 
how in contrast to this the medical 
profession occupied for a long period 
a foremost place in the Royal Society 
of London, so much so that fre- 
quently opposition was made to the 
admission of new members belong- 
ing to it (see Weld, * History of the 
Royal Society,' vol. i. chap. 4 ; vol. 
ii. p. 153). Of 5336 papers contained 
in the ' Philosophical Transactions ' 
from 1665 to 1848, 1020, the largest 
number in any department,'belonged 
to anatomy, physiology, and medi- 
cine (ibid., vol. ii. p. 565). Babbage 
complained of the influence of the 
Colleges of Physicians and Surgeons 
in the Royal Society, as occasionally 
filling the pages of the 'Transac- 
tions ' with medical papers of very 
moderate merit ; and also because 
the preponderance of the medical 
interest introduces into the Society 
some of the jealousies of that pro- 
fession (' Decline of Science in Eng- 
land,' 1830, p. 188). In the founda- 
tion of the British Association this 
union with the medical interest 
was dropped ; though the older 
" Versammlung deutscher Natur- 
forscher und Arzte," after which 
it was modelled, established and 
maintained that union. 







Into this 
Cuvier car- 
ried exact 

culties which only great zeal can surmount; we have 
to subject them to torments in order to appreciate their 
physical powers; their innermost energies only reveal 
themselves to the dissecting-knif e — only by living among 
corpses can we discover them. Among them we find the 
same spectacle as in the world, whatever moralists may 
say : they are hardly less wicked or less unhappy than 
we are; the arrogance of the strong, the meanness of 
the weak, vile rapacity, short pleasures bought by great 
efforts — death brought on by long suffering — that is the 
rule among animals as much as among men. With 
plants existence is not surrounded by pain — no sad 
image tarnishes their splendour before our eyes, nothing 
reminds us of our passions, our cares, our misfortunes — 
love is there without jealousy, beauty without vanity, 
force without tyranny, death without anguish — nothing 
resembles human nature." ^ 

Into the centre of individual and organised life — the 
life of the animal and human creation — Cuvier carried 
exact research, grounding it on the science of compara- 
tive anatomy.^ At the same time, he marked out as the 
principal problem, around which all investigations must 
turn, and upon which all classification must depend, 

ogy inarch side by side (p. vi). He 
compares natural history as a science 
with other sciences, stating that 
dynamics is become a science almost 
entirely of calculation, that cBem- 
istry is still a science altogether of 
experiments, that natural history 
will for a long time to come remain 
in most of its parts a science of ob- 
servation (p. 5) ; he maintains that 
geometry is a study of syllogisms, 
natural history a study of method 
(p. xviii). 

^ 'ElogeshistoriqueSj'vol. i. p. 91. 

2 Cuvier, in the Introduction to 
* Le R^gne animal, distribud d'apres 
son organisation, pour servir de base 
II I'histoire naturelle des animaux 
et d'introduction h. I'anatomie com- 
part' (Paris, 1817), says that for 
thirty years he had devoted to com- 
parative anatomy all his time (p. 
v), that the first results had ap- 
peared in 1795, his * Lecjons d' Ana- 
tomic comparde' in 1800 (p. vii), 
that he has made anatomy and zool- 

the phenomenon of individual life, that great vortex into 
which agencies, processes, and the elements of inorganic 
nature are continually drawn, from which they are con- 
tinually ejected, preserving not the unity of substance 
but, among changing events, the unity of form.^ 

" It is not," he says, " in the substance that in plants 
and animals the identity of the species is manifested, it is 
in the form. There are probably not two men, two oaks, 
two rose-trees, which have the compound elements of 
their bodies in the same proportion — and even these 
elements change without end, they circulate rather than 
reside in that abstract and figured space which we call 
the form ; in a few years probably there is not left one 
atom of that which constitutes our body to-day — only the 
form is persistent ; the form alone perpetuates in multiply- 
ing itself ; transmitted by the mysterious operation which 
we call generation to an endless series of individuals, it 
will attract successively to itself numberless molecules of 
different matter, all of them merely transient." ^ 

^ " La vie est done un tourbillon 
plus ou moins rapide, plus ou moins 
compliqud, dont la direction est 
constante, et qui entraine toujours 
des molecules de memes sortes, 
mais ou les molecules individuelles 
entrent et d'oii elles sortent con- 
tinuellement, de mani^re que la 
forme du corps vivant lui est plus 
essentielle que la matiere" ('R^gne 
animal,' p. 13, &c.) "II vient 
sans cesse des Elements du dehors 
en dedans : il s'en echappe du de- 
dans au dehors : toutes les parties 
sont dans un tourbillon continuel, 
qui est une condition essentielle du 
phenom^ne, et que nous ne pouvons 
suspendre longtemps sans I'arreter 
pour jamais. Les branches les plus 
simples de I'histoire naturelle par- 

VOL. I. 

ticipent dejb, h. cette complication 
et k ce mouvement perpetuel, qui 
rendent si dijficile I'application des 
sciences gdn^rales " ('Rapport,* p. 150, 
&c.) " Dans les corps vi vans chaque 
partie a sa composition propre et 
distincte ; aucune de leurs mole- 
cules ne reste en place ; toutes 
entrent et sortent successivement : 
la vie est un tourbillon continuel, 
dont la direction, toute compliquee 
qu'elle est, demeure constante, ainsi 
que I'esp^ce des molecules qui y 
sont entrainees, mais non les mole- 
cules individuelles elles-memes. . . . 
Ainsi la forme de ces corps leur est 
plus essentielle que leur matiere," 
&c. (ibid., p. 200). 

^ * Eloges historiques,' vol. iii. p. 





Keeping this unity of form, this absorbing vortex of 
life, the totality of organisation, always before him, 
Cuvier, in surveying the whole region of animated 
nature,^ fixes finally for the purposes of classification and 
division on that system of organs which expresses most 
truly the peculiarity of each of the great branches into 
which he divides the animal world — namely, the nervous 
system.^ But rather than follow him at present into the 

^ " La partie anatomique du prob- 
leme general de la vie est r^olue 
depuis longtemps pour les animaux, 
au moins pour ceux d'entre eux qui 
nous int^ressent le plus. Les voies 
que les substances y parcourent, 
sont connues ; . . . il aper9oit 
aussi comment ces routes, si com- 
pliqu^es dans I'homme, se simpli- 
fient par degr^ dans les animaux 
inf erieurs, et finissent par se reduire 
k une spongiosit^ uniforme. Les 
recherches de M. Cuvier — dans les 
le9ons d'anatomie comparde — ont 
achev^ d'assigner a chaque animal 
sa place dans la grande ^chelle des 
complications de structure" ('Rap- 
port,' p. 202, &c.) 

2 It is not my object here to give 
an account of the views of Cuvier, 
still less of his contributions to 
natural history, which — in spite of 
the special theories and laws which 
he and his followers established (see 
especially Flourens, ' Histoire des 
Travaux de Georges Cuvier,' 3*"® 
^d., 1858) — remained in his hands 
to the last pre-eminently a science 
of observation. It has been pointed 
out that Cuvier only gradually (pro- 
bably about 1812) arrived at the final 
principle of division — viz., the ner- 
vous system — and that he adopted 
it from others (notably Virey and 
De Blainville), that before 1812 he 
had successively used the organs of 
generation (1795), of nutrition, and 
of circulation as principles of clas- 
sification. In his Report of 1808, 

in mentioning his own labours, he 
says: " M. Cuvier, en ^tudiant la 
physiologie des animaux vert^bres, 
a trouve dans la quantite respective 
de leur respiration, la raison de leur 
quantity de mouvemeus, et par con- 
sequent de I'espece de ces mouve- 
mens. ... En efiet, M. Cuvier, 
ayant examind les modifications qu' 
eprouvent dans les animaux sans 
vertdbres les organes de la circula- 
tion, de la respiration, et des sensa- 
tions, et ayant calculi les resultats 
necessaires de ces modifications, en 
a ddduit une division nouvelle ou 
ces animaux sont ranges suivant 
leurs vdritables rapports" ('Rap- 
port,' p. 311, &c.) Compare also 
Carus, 'Geschichte der Zoologie,' 
Miinchen, 1872, p. 602 ; Flourens, 
" Eloge de Cuvier," in his * JLloges 
historiques,' 3™« sdrie, Paris, 1862, 
p. 122, &c. ; Hahn in the ' Grande 
EncyclopMie,' article " Cuvier." See 
also the Introduction to the ' Regne 
animal,' which proposes to arrange 
living beings according to their " or- 
ganisation," by investigating their 
•' structure," their "internal as well 
as external conformation." Cuvier 
here states that no one before had 
tried to arrange the classes and 
orders according to the " ensemble 
de la structure " (p. vi). He is thus 
led to the law of the " subordination 
des caract^res, . . . ayant soin 
d'dtablir toujours la correspond- 
ance des formes extdrieures et in- 
tdrieures qui, les unes comme les 

details of his natural history, his comparative anatomy, 
or his palaeontology, of which latter sciences he is the 
creator, it serves our present purpose better to learn how 
he viewed the object of natural science in general — how 
he defined its task. As the first step in civilisation was 
the creation of a language possessing definite rules, so 
the first step in the growth of a science is that taken by 
Linnaeus, who was not terrified by this enormous work, 
that of giving names, of framing a nomenclature.^ " But," 
says Cuvier, " to name well, you must know well. These 

autres, font partie int^grante de 
I'essence de chaque animal " (p. xiv). 
He opposes former artificial classifi- 
cations, such as the principle that 
living beings can be arranged " de 
maniere a former des etres une 
seule ligne" (p. xx). "Un etre 
organist est un tout unique, un 
ensemble de parties qui reagissent 
les unes sur les autres pour produire 
un eflfet commun. Nulle de ses 
parties ne pent done etre modifi^e 
essentiellement sans que toutes les 
autres ne s'en ressentent " (* Eloges,' 
vol. ii. p. 279). 

^ The formation of a nomencla- 
ture or a terminology is one of the 
most important steps in the begin- 
ning and the progress of science. 
Cuvier refers frequently to this: 
"Nos livres saints, a leur d^but, 
nous repre'sentent le Createur fais- 
ant passer ses ouvrages sous les 
yeux du premier homme, et lui 
ordonnant de leur imposer des 
noms. . . . Ces noms, qu'il est 
present h, I'homme d'imposer, ne 
sont pas des signes incoherens ap- 
pliques au hasard h, queiques objets 
isoles. Pour qu'ils deviennent r^- 
guliers et significatifs, ils exigent, 
comme il est dit, que les etres aient 
passe devant le nomenclateur " 
(' Eloges,' vol. iii. pp. 450, 452). No- 
where is terminology more import- 

ant than in chemistry. " L'un des 
moyeus qui ont le plus puissamment 
contribud a faciliter I'enseignement 
de la science en gdndral, et k pre- 
parer I'adoption universelle de la 
theorie nouvelle, c'est la nomen- 
clature crede par cette socidtd de 
chimiste8fran9ais. . . . Donneraux 
dldmens des noms simples ; en 
deriver, pour les combinaisons, des 
noms, qui exprimassent I'espece et 
la proportion des eldmens qui les 
constituent, c'etait offrir d'avance 
a I'esprit le tableau abregd des re- 
sultats de la science, c'etait fournir 
a la mdnioire le moyen de rappeler 
par les noms la nature meme des 
objets. C'est ce que M. Guyton 
de Morveau proposa le premier d^s 
1781, et ce qui fut completement 
execute par lui et par ses coUegues 
en, 1787" ('Rapport,' p. 88, &c.) Cf. 
* Eloges,' vol. iii. pp. 194, 482, 496. 
Cuvier (* Eloges,' vol. iii. p. 302) 
mentions ** cette antipathic pour 
les methodes et pour une nomencla- 
ture precise a laquelle Buffbn s'est 
laisse aller en tant d'endroits " ; he 
speaks of Pinel **qui avait cherchd 
d'abord a former pour les descrip- 
tions des maladies un langage pre- 
cis, modele sur celui que Linnaeus 
avait introduit en botanique" (ibid., 
voL iii. p. 386). 





beings and their parts which are to be known are to be 
counted by the million ; it is not enough to know them 
singly, for they are submitted to an order, to mutual 
relations, which must likewise be appreciated, for it is 
according to this order that each has its part to play, 
that each disappears at its tim(:, that they reappear simi- 
larly made, always in the same proportions, and armed 
with the necessary forces and faculties for the main- 
tenance of these proportions, and of the whole of this 
perpetual vortex. Not only is each being an organism, 
the whole universe is one, but many million times more 
complicated; and that which the anatomist does for 
a single animal — for the microcosm — the naturalist is 
to do for the macrocosm, for the universal animal, 
for the play of this alarming aggregation of partial 

organisms." ^ 

It was this sustained regard for the value of detailed 
research and minute observation, coupled with an equal 
appreciation of the unity of all regions of existence, 
and all branches of learning, that elevated Cuvier to 
the height of the science of his age and his country, 
and made him a true exponent of the modern scientific 
spirit. The works of Newton and Laplace may contain 
more formulae of lasting value, more instruments of per- 
manent scientific use— they may, for all time, have traced 
a few lines of the enwoven cipher of the all-pervading 
mechanism of nature ; it is, however, well to note that he 
only who keeps in steadfast view the life rather than the 
mechanism of existence, approaches the great secret of 
nature, and gauges rightly the value of each component 

1 Cuvier, *Eloges historiques, ' vol. iii. p. 453. 

part, or the worth of each human effort.^ In this respect 
the nineteenth century knows no greater figure than 
Cuvier ; not even Humboldt, great and comprehensive as 
was his scientific view. The advantages also of Cuvier's 
position as permanent Secretary of the French Academy 
of Sciences were exceptional, and well fitted to bring out 
his extraordinary talents. We can say that in him science 
has become fully conscious of its true methods, its useful- • 
ness, its most becoming style, its inherent dignity, its past 
errors, its present triumphs, the endless career which lies 
before it, and the limits which it cannot transgress. 
Educated in Germany, at the same school as Schiller 


and Dannecker,^ imbued by early experience and by training, 

^ " C'est la continuation de ce com- 
mandement de voir et de nommer, 
par oil s'ouvre la vie de notre esp^ce, 
c'est la voie qui devait nous con- 
duire soit a des contemplations plus 
hautes, soit seulement h. des inven- 
tions utiles. En effet I'histoire 
naturelle ne fait aucun pas sans 
que la physiologie et la philosophic 
gendrale marchent d'un pas ^gal, 
et sans que la societ,^ receive leur 
tribut commun" ('Eloges,* vol. iii. 
p. 474). 

2 Cuvier has himself written an 
account of his early life and studies. 
It is given by Flourens, ' Eloges,' vol. 
i. pp. 167-193. He was born in 1769, 
of a Protestant stock, at Mont- 
beliard, the capital of a small prin- 
cipality, situated in the Jura, and 
then belonging to Wiir tern berg. 
The autocratic Duke Charles (1737- 
1793) had founded a military acad- 
emy in Stuttgart, his capital, where 
400 youths were at his expense 
housed and educated according to 
a strict rule, but under the guid- 
ance of enlightened masters, and in 
a thoroughly modern spirit. The 
institutipn was a kind of oppo- 

sition to the Protestant Church 
rule, which had very early spread 
a system of popular and compulsory 
education throughout the country. 
It is a chapter of history well worth 
reading. The great problems of 
popular education as against higher 
instruction, Protestant discipline in 
the lower as against military dis- 
cipline in the higher schools, the 
democratic as against the aristo- 
cratic spirit, the independence as 
against the State - regulation of 
University teaching, were fought 
out by the dukes and the Estates 
of Wiirtemberg in a prolonged war- 
fare, a sample of similar movements 
all over Germany, and well told by 
Perthes in his * Politische Zustande 
und Personen in Deutschland zur 
Zeit der franzosischen Herrschaft' 
(Gotha, 1862, pp. 501-548). Cuvier 
evidently saw the better side of the 
system, for he entered after the 
imperious character of the duke 
had been subdued by the victorious 
estates. Forced to change his ways, 
which he conscientiously ^id, the 
duke laid by for his country, as a 
local historian says, " a fund of in- 




personal contact with that spirit of general education 
and universal training which then animated the German- 
speaking nations of the Continent, thoroughly grounded 
in classics and mathematics, with a cosmopolitan know- 
ledge of languages and literature, which fitted him to 
understand the merits of different nations, he became 
the great exponent of that peculiar system of higher 
culture which since the time of Colbert the French had 
elaborated— the academic system.^ The centre of this 

telligence and acquisitions by which 
we have benefited up to modern 
times" (Perthes, p. 510). We know 
the other and older side of the 
picture from the ' Life of Schiller ' 
(see, inter alia, Carlyle, *Life of 
Schiller,' collected works, library 
edition, vol. v. p. 258). Cuvier 
gives a long description of the " Karl- 
schule " : " C'etait un etablisse- 
ment vraiment magnifique. Envi- 
ron quatre cents boursiers et pen- 
sionnaires, loges dans un edifice tel 
qu'il n'y en a aucun d'approchant 
en Europe (parmi ceux qui sont 
consacres a I'instruction de la jeun- 
esse), vetus d'un bel uniforme, con- 
duits par des officiers et des sous- 
officiers tir^s des regiments du due, 
recevaient des lemons de tout genre 
de plus de quatre-vingts maitres ou 
professeurs. On a beaucoup parl^ 
de I'esprit de despotisme avec lequel 
le due disposait de leurs personnes 
et choisissait pour chacun d'eux 
r^tat qu'il devait embrasser, et je 
crois en efifet qu'il en etait ainsi 
dans I'origine de I'etablissement ; 
mais de mon temps, je n'ai rien 
vu de semblable, et ce qui est cer- 
tain, c'est que personne ne pretendit 
meme me donner de conseil Ji cet 
egard. II y avait cinq facultes 
superieures, droit, medecine, admin- 
istration, militaire et commerce" 
(Flourens, loc. cit., p. 171). 

1 The first great representative 

of this academic spirit and culture 
was Fontenelle, who, living during 
a hundred years, from 1657 to 1757, 
was Secretary of the Academie des 
Sciences during forty -two years, 
from 1699 (the year of the recon- 
stitution of the Academy) to 1741. 
Among his successors were men like 
Condorcet, Delambre, Cuvier, and 
Arago. Fontenelle gave to scien- 
tific subjects a dignified popularity, 
separated the departments of science 
and metaphysics, kept the scientific 
interest free from the commercial, 
and through his connection with the 
Academie fran9aise did probably 
more than any other writer to es- 
tablish that superiority of style and 
diction for which the great French 
men of science are so remarkable and 
so superior to those of other coun- 
tries. Bertrand, himself a successor 
of Fontenelle, says of him : " Pr^tant 
aux travaux de ses confreres la 
finesse de ses aper9us et la vivacite 
ingenieuse de son style, il a su dans 
leurs portraits, qui sont des chefs- 
d'oeuvre, plus encore que dans I'ana- 
lyse de leurs d^ouvertes, donner 
aux plus humbles et aux plus 
modestes une celebrite imprevue 
et durable, et le juste et serieux 
hommage qu'il rend au vrai merite 
fait aimer et respecter tout h la fois 
les savants et la science" (*L' Aca- 
demie des Sciences et les Academi- 
ciens,' p. 113). See also Voltaire's 



system was the old Academy of Sciences, which, with 
a short interruption during the storm of the Eevolution, 
survived,^ and formed the principal feature in the Insti- 
tute. Allied with this institution, and directly inspired 
by its spirit, were the great schools of natural science, the 
great collections of natural objects, latterly also the great 
medical institutions of Paris. It professed to protect 
scientific studies in a royal and generous manner, at- 
tracted talent from outside, rewarded foreign as well as 
French research,^ and tried to keep the scientific spirit 
of inquiry, as well as the form in which it found 
expression, pure and undefiled.^ It favoured the co- 

; Cabanis, 
Medecine ' 

'Si^cle de Louis XIV.' 
' Revolutions de la 
(CEuvres, Paris, 1823, vol. i. p. 200); 
Flourens, ' Eloges historiques,' vol. 
iii. p. 31, &c. ; Maury, * Les Aca- 
demies d'autrefois,' vol. i. p., 153, 
163 et passim; Bouillier, 'Eloges 
de Fontenelle,' Introduction. 

1 " Tandis que tout a ete renou- 
vele dans la politique et les moeurs 
publiques ... la vie scientifique 
et litteraire a gensiblement garde sa 
constitution. . . , Le College de 
France, I'Academie fran9ai8e, 1' Aca- 
demie des Inscriptions et Belles- 
lettres, I'Academie des Sciences, la 
Bibliotheque imperiale, I'Observa- 
toire, le Museum d'Histoire natur- 
elle, subsistent encore, comme au 
siecle dernier, et dans nos provinces, 
une foule d'academies sont d'une 
creation anterieure k 1789" (Maury, 
loc. cit., p. 1). 

2 " Euler f ut quatre fois couronne 
pour des questions de physique et 
de mathematiques. . . . Daniel 
Bernoulli obtint le prix dix fois" 
(Maury,, p. 171). Among the cele- 
brated Eloges by Fontenelle there 
are those of Leibniz, of Peter the 
Great, of Newton, of Marsigli, of 
Boerhaave ; among those by Con- 

dorcet there are those of Haller, 
Linnaeus, Hunter, and Euler ; among 
Cuvier's there are those of Gilbert, 
Priestley, De Saussure, Cavendish, 
Pallas, Rumford, Werner, Banks, 
and Davy. 

^ "Jusqu'^ present," says Fon- 
tenelle in 1699, "TAcademie des 
Sciences ne prend la nature que 
par petites parcelles. Nul systfeme 
general, de peur de tomber dans 
I'inconvenient des syst^mes pr^ci- 
pit^s dont I'impatience de I'esprit 
humain ne s'accommode que trop 
bien, et qui, etant une fois etablis, 
s'opposent aux verites qui syrvien- 
nent" (quoted by Flourens, * Eloges,* 
vol. iii. p. 19). " L'esprit de I'Acad- 
emie des Sciences a done tou jours ete 
I'esprit d'experience, d'etude directe, 
d'observation precise, I'amour de la 
certitude. D'abord cartesienne, elle 
devint ensuite Newtonienne, " &c. 
(ibid., p. 21). Fontenelle contrasts 
the " philosophie des mots et celle 
des choses, de I'Ecole et de I'Aca- 
demie" ('Eloge de Du Hamel' in 
Bouillier, p. 10). "Fontenelle se 
plait k multiplier les exemples de 
cette incapacite chez les savants de 
faire fortune et de ce noble des- 
int^ressement." " II aimait mieux 







Cuvier the 
tive of the 

operation of many minds in rearing the great edifice of 
science, and found a place for the minutest research, as 
well as a field for the development and sway of great and 
governing ideas. Of the best form of this spirit and 
system — the Academic — Cuvier was the greatest repre- 
sentative. Through several dozen illoges which he pro- 
nounced on the decease of a number of the most illus- 
trious scientific men of Europe, as well as through 
several Keports, in which he summed up the labours and 
progress of his age, and the peculiar features of his period, 
he affords to the student of history an insight into that 
distinctive phase which scientific thought had entered in 
France at the end of the eighteenth century. This he 
allows us to contrast with other phases of thought, such 
as the philosophical or individual, which obtained in other 
ages or countries, and suggests as well as gives the means of 
answering the question, to what extent the scientific ideal 

etudier que subsister," he said of 
one of the Academicians (Bouillier, 
pp. ix, xii). Cuvier was very watch- 
ful over the Academy in keeping 
out the speculative spirit. See 
what he says in the joint Report 
on geology with Haiiy and Leli^vre 
(' Mem. de I'lnstitut,' vol. viii. 1607, 
p. 136). "Que doivent done faire 
lea corps savans pour procurer a une 
science aussi interessante et aussi 
utile, les accroissemens dont elle est 
susceptible ? ... lis doivent tenir 
la conduite, qu'ils ont tenue depuis 
leur etablissement, a I'egard de 
toutes les autres sciences : encour- 
ager de leurs ^loges ceux qui con- 
statent des faits positifs et garder 
un silence absolu sur les syst^mes 
qui se succMent." Compare with 
this what he says about the use of 
the principle of "vital force," al- 
ways referring to Newton's method 

('M^m. de I'lnst.,' vol. vii. p. 77, 
&c.), further in his analysis of Gall 
and Spurzheim's Memoire (' M^m. 
de I'Inst.,' vol. ix. p. 65): "Les 
commissaires de la classe . . . ont 
donn^ leur assentiment a presque 
toutes les propositions de MM. G. 
& S., qui ne dependent que de 
I'inspection anatomique, &c. . . . 
les commissaires ont cru dgale- 
ment de leur devoir de prevenir le 
public, qu'il n'y a aucun rapport 
direct, aucune liaison necessaire 
entre ces decouvertes et le doctrine 
enseign^ par MM. G. & S., &c. . . . 
Toutes ces matieres sont encore trop 
etrangeres aux attributions de la 
classe, elles tiennent aux faits sen- 
sibles d'une mani^re trop l&che, 
elles pretent li trop de discussions 

of the end of this century agrees with or differs from that 
of its beginning. Upholding the Newtonian rather than 
the Baconian and Leibnizian standard in the mathemati- 
cal and physical sciences,^ he has marked that line which 
our whole century has contributed to trace out more dis- 
tinctly ; whilst, as regards the purely natural sciences, his 
continued emphasising of the great problem of organisation, 
and his later controversy with Geoffroy de Saint-Hilaire, 
mark that point in which this century has most distinctly 
departed from the prevailing ideas of its early years.^ 
He also recognised earlier than any other mind of similar 
eminence what our century increasingly realises, how, 
without a system of condensation, contained in reports, 
statistics, and figures, aided by classifications and systems, 
the growing bulk of accumulated knowledge becomes 
chaotic and unmanageable.^ 


vagues, pour qu'un corps tel 
le notre doive s'en occuper 


^ Cuvier was not brought up in 
the school of the Encyclopaedists, 
and I cannot find that he attached 
the great importance to the writ- 
ings of Bacon which that school 
commonly did. As to Newton and 
Leibniz, he contrasts their methods, 
considering them " comme les chefs 
et les representans des deux 
m^thodes opposees qui se sont dis- 
pute I'empire de la science " (' His- 
toire des Sciences naturelles,' 
publiee par Magdeleine de Saiut- 
Agy, Paris, 1841, vol. iii. p. 19, 
&c.) See also in his joint Report 
with Haiiy and Lelievre on the 
Science of Geology (' Mem. de I'ln- 
stitut,' 1807, p. 133): *'0n yit 
renaitre dans cette partie de I'his- 
toire naturelle la m^thode syst^ma- 
tique de Descartes, que Newton 
semblait avoir bannie pour jamais 
de toutes les sciences physiques, 
. . . et lorsqu'on songe que Leib- 
niz et Buffon sont au nombre 

des philosophes dont je parle ici," 

2 A future chapter will deal speci- 
ally with this subject. Cuvier, as 
is well known, maintained the fixity 
of species, and opposed the theories 
of St Hilaire and Lamarck, in which 
a later generation recognises the 
beginnings of the Darwinian doc- 
trine of the transmutation of species. 
"On est oblige d'admettre certaines 
formes, qui se sont perpdtu^es 
depuis I'origine des choses, sans 
exceder ces limites ; 
etres appartenans k 
formes constituent 
appelle une espece" 
mal,' vol. i. p. 20). 

3 Cuvier was the first great scien- 
tific writer who undertook to give 
a historical survey of the position 
of the different natural sciences, 
with a view of ascertaining what 
had been achieved and what re- 
mained to be done. He did what 

et tous les 
Tune de ces 
ce que Ton 
('R^gne ani- 






On the 

Cuvier had also a true historical sense, which enabled 
him to trace the connection of science with political 
history, with literature, with the fine and useful arts. 
And he helps to answer a question which to us is of 
forties of paramount interest, How did science fare during the 
i^gthtiT crreat cataclysm of the Kevolution ? how under the reac- 

volution and ® "^ -.^. -r^ • « -r» p 4.4. ,^^4- 

Em^ tionary despotism of the First Empire ? Before attempt- 
ing to reply to these questions in the light of subse- 
quent and general European history, I will select a few 
passages from Cuvier which throw light upon these 

points : ^ — 

"There is always a revolution required in order to 

change habits which have become general, and the most 
necessary revolutions do not take place without some 
circumstance, which is sometimes long delayed. We 
have been able to see how in such a case everything 
furthers the sciences, even the delays and contrarieties 
which they seem to suffer under. 

" The events which disturbed the world, and which for 
natural science temporarily dried up the sources of its 
riches,^ obliged it to return to itself, and to make a new 
study of what it possessed, more fruitful than the most 

a generation later the British Asso- 
ciation undertook to do, and what 
in Germany the many "Jahres- 
berichte*' do nowadays. See his 
" Analyse des Travaux," &c., ' Mem. 
de I'Institut,' vol. ix. p. 53, and his 
celebrated * Rapport historique sur 
le Progres des Sciences naturelles 
depuis 1789,' Paris, 1810. 

^ * Eloges historiques,' vol. iii. p. 
456, 1824. 

2 This refers to the isolation of 
France during the war and the Con- 
tinental blockade, which deprived 

it of foreign imports and the scien- 
tific collections of foreign specimens ; 
see also 'Eloges,' vol. i. p. 9 ; vol. iii. 
p. 202: "Quand la jalousie des 
peuples nous privait des produits 
Strangers, la chimie les faisait dclore 
de notre sol." "Le conseil des 
mines ^tabli en 1793, lorsque I'in- 
terruption de tout rapport avec 
I'etranger fit sentir le besoin de 
tirer parti de notre territoire a 
donn^ h. ces sortes de recherches 
une impulsion toute nouvelle" 
('Rapport,' p. 178). 

fortunate departures could have been. During this ap- 
parent rest, all the different parts of method were deep- 
ened ; the interior of natural objects was studied ; even 
minerals were dissected and reduced to their mechanical 
elements ; a still more intimate analysis was made by a 
perfected chemistry; the earth itself was, during this 
interval, if the expression is allowable, dissected by the 
geologists ; its depths were sounded ; the order and layers 
of rock which form its shell were recognised.-^ In the 
absence of foreign contributions the interior of the soil 
on which we walk became tributary to science. The 
beings of which it contains the remains came to light, 
and revealed a natural history anterior to that of to- 
day, different in its forms, and nevertheless subject to 
similar laws, thus giving to these laws a sanction which 
no one expected. The botanists did not gather so many 
plants in their collections, but with the lens in hand they 
demonstrated more and more the intimate structure of 
the fruit, the seed, the various relations which connect 
the parts of the flower, and the indications which these 
relations furnish for a natural division. The most deli- 
cate forms of organic tissues were exhibited; medicine 

^ Cuvier refers here to the inves- 
tigation of the fossils in the Paris 
basin, which he undertook during 
the years 1804 to 1808 : " La singu- 
larity des animaux dont je decouv- 
rais les ossements a Montmartre 
me fit desirer de connaitre plus en 
detail la composition geologique des 
environs de Paris. Mon ami Brong- 
niart s'associa a moi pour ce travail ; 
nous fimes ensemble et s^pardment 
beaucoup de courses. . . . Ces 
recherches ont donne une face toute 
nouvelle a la geologic, et ont occa- 

sionnd toutes celles qu'ont faites 
ensuite en Angleterre MM. Webster, 
Buckland, Labeche et autres" 
(Cuvier, "M^m. sur sa Vie" in 
Flourens; 'Eloges,' vol. iii. p. 188). 
This was the beginning of the 
Science of Palaeontology, a term 
which Cuvier did not use himself 
(Flourens, ' Travaux de Cuvier,' p. 
147). See also Cuvier, ' Recherches 
sur les Ossemens fossils de Quadru- 
pedes,' &c., 1st ed., 1812, 3rd ed., 
1825, in the Introduction. 



and chemistry united their efforts to appreciate in the 
minutest detail the action of external elements on the 
living organism.^ The different combinations of organs, 
or what we call the different classes, the different genera, 
were not less studied than general theories. There were 
no animals, ever so small, the inner parts of which, 
unveiled by anatomy, did not become known as well 
as our own. Every organic system was likewise sub- 
mitted to a special examination. The brain, marking 
the degree of intellectual power; the teeth, signs of 
the nature and energy of the digestive forces ; the bony 
system, above all, which is the support of all others, 
and which determines the connected forms of animals, 
—all these were followed into the smallest species and 
into the minutest parts. We see how, after such studies, 
there could be no more talk of superficial or artificial 
methods. The old natural history had ceased to rule. 
It was not that old natural history any more, but a 
science full of life and youth, armed with quite novel 
ways and means, which beheld the world reopened by 

the Peace." ^ 

In an earlier passage,^ speaking of the reopening of 
academies and schools by the Government of the Kevolu- 

1 Compare with this the 'Rap- 
port* of the year 1808, p. 201, &c. 
The above remarks refer mainly to 
Bichat. "Bichat a donn^ h I'ana- 
tomie un grand int^ret, par I'opposi- 
tion de structure et de forme qu'il 
a d^velopp^, entre les organes de 
la vie animale, c'est-k-dire, du senti- 
ment et du mouvement, et ceux de 
la vie purement v^g^tative. . . . 
L'attention particuli^re donnee par 
Bichat au tissu et aux fonctions des 
diverses membranes, et I'analogie 

qu'il a etablie entre celles de parties 
tr^s ^oignees, ont jete aussi des 
lumi^res nouvelles sur I'anatomie, 
principalement dans ses rapports 
avec la medecine" ('Rapport,' p. 

2 This refers to the peace which 
concluded the Napoleonic wars, and 
re-established the free intercourse 
of France with, the rest of the world. 

3 In the 'Eloge of Fourcroy," 
of the year 1811 ('Eloges,' vol. ii. 
p. 40, &c.) 



tion, Cuvier remarks : " It was not merely a question of 
isolated discoveries, but of institutions, which, in assuring 
the conservation of the sciences, would multiply their 
progress indefinitely. What was needed was no longer a 
simple experimenter, master of his subject and his instru- 
ments, it was a man obliged to battle against all kinds of 
obstacles, and to benefit his fellow-citizens, mostly in spite 
of themselves. The Convention had destroyed academies, 
colleges, universities; nobody would have dared to ask 
boldly for their restitution ; but soon the effects of their 
suppression showed themselves in the most susceptible 
point; the armies were without doctors and surgeons, 
and these could not be created without schools.^ But 
who would believe that time was required to give courage 
enough to call them schools of medicine. Doctor and 
surgeon were titles too contrary to equality, apparently 
because there is no authority over the patient more neces- 
sary than that of the doctor; therefore the odd term 
" schools of health " was used, and there was no question 
of either examination or diploma for the students. In 
spite of this, a penetrating glance reveals, in the regula- 
tions which were carried, the intentions of him (Fourcroy) 
who drew them up. The three great schools founded at 

1 See 'Eloges,' vol. i. p. 353. 
"Cependant les gens qui avaient 
fait toutes ces suppressions eurent 
promptement lieu de s'apercevoir 
que, s'il ^tait h la rigueur superflu 
d'apprendre toute autre chose, on 
ne pouvait gu^re se dispenser d'ap- 
prendre la medecine. Toute la 
France se pr^cipitait aux frontieres, 
et, apres des prodiges inouis de 
d^vouement et de valeur, les ddfen- 
seurs de la patrie ne trouvaient 

aucun secours pour leurs blessures 
et pour leurs maladies. On com- 
menga done par I'drection des ecoles 
de medecine cette longue suite de 
restaurations, que I'dtablissement 
de I'universit^ vient de couronner 
et de lier en un ensemble aussi 
imposant par I'etendue de son plan 
que par la vigueur de son organisa- 
tion." See also 'Rapport,' &c., p. 




France has 
done more 
than other 
countries to 


between the 
literary and 
the national 

this epoch ,^ received an abundance of means, of which 
up to that time there was no idea in France, and which 
still form the finest ornament of the University.'* 

Similar passages might be collected in which Cuvier 
enlarges on the influence of war and revolutions, of the 
Continental blockade and the isolation of the country ; on 
the reconstruction of hospitals and the admission of medi- 
cal science into the Academy ; on the creation of new 
industries ; on the development of the mining and mineral 
wealth of the country ; on the scientific value of colonies 
and travels, and many other interesting topics. In con- 
fining myself more closely to the history of thought and 
the growth of the modern scientific spirit, I will make 
some reflections which his remarks force upon us. 

I have noted above how France more than any other 
country worked for the popularisation of science, how her 
polite literature alone during the eighteenth century bears 
the strong impress of modern scientific ideas ; no other 
country has a Fontenelle, a Voltaire, a Buffon. This 
peculiarity must be recognised as a very powerful and 
valuable stimulus to the growth of the scientific spirit 
It emanates largely, if not ^exclusively, from the peculiar 
position of the old Academy of Science. It must, how- 
ever, not be forgotten that it was not a popularisation of 
the kind we witness nowadays. 

The class of literature which in our age spreads broad- 
cast the discoveries or ideas of science ; the endless num- 
ber of magazines, reviews, and daily papers; the small 
treatises, the cheap primers, the compact text-books, did 

^ They were the three " Ecoles de 
Sant^" at Paris, Strasbourg, and 
Montpellier (see Hippe»u, *L'In- 

struction publique en France,' vol. 
ii. p. 194). 



not then exist.^ Science was not a subject of general, still 
less of popular, instruction. It was an occupation of the 
few, who, privileged by fortune or talent, or gifted with 
inordinate perseverance, forced their way into the salons 
of society^ or the rooms of the Academy. The first public 
course of natural history was opened in Paris by Valmont 
de Bomare in 1 7 6 0.^ Science still stood far out of the reach 
of the practical man or the poor man; it had not yet 
become an element of education or an instrument for 
industry. It was a fashionable pursuit, a luxury of the 
great, a key that occasionally opened the door of the 
palace ; but it was not a thing of immediate use, except 
in adding glory and renown to its royal protectors, or 
to the rare genius which could make new discoveries. 
Almost the only application made of it was in naviga- 
tion, and in the construction of instruments connected 
therewith. This essentially literary — not national — 
popularisation of science had also its great dangers. 34. 

. Dangers of 

No ideas lend themselves to such easy, but likewise to the merely 

" literary pop- 

such shallow, generalisations as those of science. Once uiarisation. 
let out of the hand which uses them, in the strict and 
cautious manner by which alone they lead to valuable 
results, they are apt to work mischief. / Because the tool 
is so sharp, the object to which it is applied seems to be 

^ Cuvier, in his ' Rapport,' &c., p. 
361, mentions the elementary works 
published by some of the medical 
professors at the beginning of the 
century, but says also that " En 
AUemagne, surtout, oti I'usage des 
livres ^l^mentaires est plus commun 
que chez nous, il n'est presque 
aucune university, dont les profes- 
seurs n'en aient public d'excel- 

**^ See Maury, p. 182, &c. Also Cu- 
vier, ' Rapport,' vol. ii. p. 427 : " En 
France la reputation des ouvi-ages 
depend, pour I'ordinaire, des femmes 
et de quelques gens de lettres, qui 
croient pouvoir juger des sciences 
positives, parce qu'ils ont combing 
quelques idees g^nerales de m^ta- 

•* See Maury, *L'ancienne Acad- 
^mie des Sciences,' p. 283, 





SO easily handled. The correct use of scientific ideas is 
only learned by patient training, and should be governed 
by the not easily acquired habit of self-restraint. It is 
well known how the fundamental notions of a mechanical 
science, let loose into literature by Fontenelle, by D'Alem- 
bert, by Condorcet, or absorbed by Voltaire and Diderot, 
were expanded into a system of materialistic philosophy 
in ' L'Homme Machine,' the ' Systeme de la Nature,' and 
other works, the extreme views of which the great scien- 
tific thinkers could hardly approve of.^ These hasty but 

^ As a great deal of confusion ex- 
isted for a long time in European 
literature as to the exact succession 
in time of the different works which 
assisted to spread mechanical views 
of the world and of life, I put down 
the main dates : — 

Fontenelle (1657-1757) published 
his Eloges of the great Academi- 
cians, in which the principles of 
the philosophy of Descartes, Leib- 
niz, and Newton were popularly- 
expounded and discussed, from 
1700 onward. His 'Plurality des 
Mondes' had appeared already in 
1686 ; it had 'popularised Cartesian 


Voltaire (1694-1778) published 
his 'El^mens de la Philosophic de 
Newton' in 1738. 

La Mettrie (1709-51) published 
his 'Histoire naturelle de I'Ame' 
in 1745, and his * L'Homme 
Machine' in 1748. 

D'Alembert and Diderot pub- 
lished the first volume of the ' En- 
cyclopedic' in 1751. 

Buffon (1707-88) published, 1749, 
his * Th^rie de la Terre,' being the 
first portion of the ' Histoire natur- 

Holbach (1723-89) published 
under the name of Mirabaud, 
1770, the 'Systeme de la Nature.' 

Of these works, the three which 

created the greatest popular sensa- 
tion— riz., VolUire's ' Elemens,' 
La Mettrie's ' L'Homme Machine,' 
and Holbach's ' Systeme '—were all 
published in Holland. Voltaire, 
D'Alembert, and Diderot appear to 
have approached philosophical prob- 
lems mainly from the position of 
Newton's natural philosophy, La 
Mettrie from the teachings of the 
great Boerhaave, Holbach princi- 
pally from a study of chemistry. 
It is unnecessary to say that none 
of them had the sanction of their 
great masters for the applications 
they made of principles which had 
been established and used for special 
scientific purposes. And the same 
may be said with reference to the 
influence of Locke, which in almost 
all the instances mentioned was 
combined with that of the great 
naturalists. But this does not be- 
long to the line of thought in which 
we are interested at present. For 
the sake of completeness only I 
mention that Locke's teachings as 
well as Newton's were made popu- 
larly known in France by Voltaire's 
" Lettres sur les Anglais ' (burnt by 
order of the Parliament of Paris in 
1734), whereas Condillac's (1714-80) 
more systematic treatise, entitled 
humaines,' appeared in 1746. It is 

brilliant generalisations, expressed frequently in the most 
perfect language, did no good to the truly scientific cause ; 
they did not spread the genuine scientific spirit. Much 
of the good done by Fontenelle, by Voltaire, by Buifon, 
was spoiled or neutralised by premature and ill-founded 
theories. How much, or how little, they contributed 
(either directly or by a kind of reaction which set in 
against them, of which Eousseau may be regarded as the 
centre) to bring about the Eevolution is a matter of 
much controversy; certain it is that the Eevolution 
broke their sway, and destroyed their immediate influ- 
ence.^ To the purely literary the Eevolution added 

important, in dealing with the ex- 
treme materialistic writings which 
French literature produced between 
1745 and 1770, to keep distinct the 
different origins from which they 
started, and the different influences 
which combined to produce them : 
the mathematical and mechanical 
principles borrowed from Newton, 
the physiological and medical eman- 
ating from Linnaeus and Boerhaave, 
and the psychological coming from 
Locke and Shaftesbury. Lange, in 
his ' History of Materialism ' (transl. 
by Thomas, London, 1880, 3 vols.), 
was the first to point out clearly the 
correct chronology and succession 
of these writings (see especially vol. 
ii. pp. 49-123), and to dispel the 
misconceptions which, since the ap- 
pearance of Hegel's ' Geschichte der 
Philosophie' in 1833-36, had passed 
through nearly all historical works 
published in Germany. From his 
exhaustive references, it is evident 
that the extreme views of La 
Mettrie, Diderot, and Holbach can- 
not be fathered on any of the great 
scientists or philosophers, but were 
an attempt to apply scientific prin- 
ciples to the solution of philosophi- 
cal, ethical, or religious questions, 


frequently for practical and politi- 
cal purposes. 

^ It would probably be more 
correct to say that these daring 
attempts to deal with the general 
problems of knowing and being, 
with the nature of the soul and the 
conduct of life, were discarded as 
premature, and that the followers 
of Condillac and Locke betook them- 
selves to a more patient study of 
the facts of the inner life, as the 
followers of Buffon forsook his bril- 
liant generalisations for the more 
patient and fruitful study of all 
the forms of physical nature. And 
in this respect the Government of 
the Revolution took a memorable 
step when it founded on the 3rd 
brumaire, an iv. (25th October 
1795), on a Report of Daunou, 
based mainly on ideas expounded 
by Condorcet, the "Academic des 
Sciences morales et politiques." It 
was the intention to abandon meta- 
physical generalisations, and to com- 
bine the scientific and historical 
spirit in the study of mental, 
moral, and social phenomena, draw- 
ing extensively on the assistance of 
the medical sciences, or a know- 
ledge of human nature in its nor* 



The Revolu- 
tion added 
the modem 
tion of 



something different—*!^., the modern practical popular- 
isation of science : it established its educational and its 
technical importance. Science was to be not an elegant 
amusement, or a refined luxury, nor even exclusively 
the serious occupation of the rare genius : it was to be 
the basis of a national instruction, and the foundation 
of the greatness and wealth of the nation. The Memoirs 
of the Academy were cleansed of all dangerous general- 
isations which might have brought them into touch with 
political controversy ; the language was confined to the 
measured and concise statement of facts, or to theories 
capable of mathematical verification and treatment ; con- 
jectural matter was carefully excluded, and a standard of 
scientific excellence, both in matter and form, was raised, 
to which we still look up with admiration.^ At the same 
time, this lofty and dignified spirit enlivened the courses 

mal and diseased conditions. This 
organiftation produced, during its 
short existence of only seven years, 
8ome memorable works; but its 
position was for various reasons 
secondary only : it was eclipsed by 
the European renown which the 
" Academie dee Sciences " possessed, 
owing to its historical antecedents 
and its brilliant discoveries and the 
practical usefulness of its labours. 
But the idea of including ethical 
and political studies under the term 
"Science," due probably to Con- 
dorcet, was fixed by this organisa- 
tion, and has in the course of the 
century acquired increasing influ- 
ence. From these beginnings we 
shall have to study ite career m an- 
other portion of the present work. 

1 According to Cuvier, " la langue 
naturelle de 1' Academie des Sci- 
ences" is "la langue des chiffres" 
CEloges,' vol. i. p. 24); "1' Acade- 
mic a toujours eu pour principe de 

ne se rendre qu'a des calculs ou a des 
experiences positives" (vol. iii. p. 12). 
Compare also * Mem. de I'lnstitut,' 
vol. vii. p. 77, where he speaks of 
the method of Newton, showing 
how little the employment of a 
principle like that of " vital force" 
in physiology can be compared with 
that of gravitation, employed by 
Newton to explain the movement 
of the heavenly bodies ; again, vol. 
viii. p. 139, where he refers to the 
great service rendered by the Aca- 
demy, "s'il parvenait a diriger les 
esprits vers des recherches positives, 
mais longues et p^nibles." And 
vol. ix. p. 61: "On aime toujours 
h voir se multiplier dans les sciences 
exp^rimentales les moyens simples 
d'arriver b, la precision et de se 
rapprocher des sciences mathema- 
tiques," and other passages quoted 
above, p. 115 and p. 128. See also 
his remarks on the Philosophy of 
Nature, 'Rapport,' p. 335. 


of lectures delivered in the great schools by the first men 
of the nation, and became, through them, the habit of a 
large number of ardent pupils, who were to carry it fur- 
ther into more popular teaching, or into the applications 
of art and industry.^ The results of both are well known. 
We still live, at the end of the century, under their im- 
mediate influence. If now we continually appeal to scien- 
tific authorities for aid in the solution of practical prob- 
lems, it is well to remember that nothing helped more to 
raise science to the eminence of a great social power than 
the action of the Eevolutionary Government in 1793. 
Whilst it guillotined Lavoisier, Bailly, and Cousin ; drove 
Condorcet to suicide, and others like Vicq-d'Azyr and 
Dionis du Sejour into premature death ;Mt had to ap- 

^ See Cuvier, " Reflexions sur les 
Sciences," 1816, in * Eloges,' &c., 
vol. i. p. 24, &c. : "Que Ton re- 
cherche, ce qu'ont valu h la France 
depuis vingt ana les inventions 
pratiques deriv^es des d^ouvertes 
de MM. Berthollet, Chaptal, Vau- 
quelin, Thenard, &c. , dans la seule 
chimie minerale, dans cette branche 
assez bornee des sciences physiques ; 
I'extraction de la soude, la fabrica- 
tion de I'alun, du sel ammoniac, des 
oxydes de plomb, des acides mine- 
raux, toutes substances que nous 
tirions de I'^tranger ; I'epuration 
des fers, la cementation de I'acier 
et enfin le ddveloppement des arts 
qui emploient ces matidres premi- 
eres : il est clair que c'est par cen- 
taines de millions qu'il faudra cal- 
culer." Also, vol. iii. p. 202 : " Les 
applications de la science h, la pra- 
tique avaient fait de M. Berthollet, 
lorsque la guerre de la revolution 
^clata, le chimiste le plus connu du 
public, apr^s Lavoisier; et il etait 
presque impossible que Ton ne re- 
courat pas a lui au moment ou la 

chimie devint pour la guerre un 
auxiliaire de premiere necessity, et 
lorsqu'il fallut demander h notre 
sol le salpetre, la potasse et jus- 
qu'aux mati^res colorantes ; qu'il 
fallut apprendre a faire en quelques 
jours toutes les operations des arts. 
Chacun se souvient de cette prodi- 
gieuse et subite activite qui etonna 
I'Europe, et arracha des ^loges 
meme aux ennemis qu'elle arreta. 
M. Berthollet et son ami M. Monge 
en furent I'Ame." 

2 Vicq-d'Azyr (1748-94), the great 
forerunner of Cuvier in the new 
science of comparative anatomy, 
"au sortir d'une de ces parodies 
sinistres d^corees du nom de fete 
nationale, ^tait saisi d'un mal qui 
I'enlevait en quelques instants dans 
le d^lire de la peur. Dionis du 
Sejour (1734-94), apres deux anndes 
d'effroi et de misere, ne trouvait 
plus assez de force pour gotiter les 
temps moins malheureux amends 
par la chute de Robespierre" 
(Maury, 'Les Academies d'autre- 
fois,' vol. i. p. 332). 


peal for its most necessary requirements to the society 
of scientific authorities, which it professed not to need. 
" Everything," says the historian of the Academy, was 
wanting for the defence of the country-powder, cannons, 
provisions. The arsenals were empty, steel was no longer 
imported from abroad, saltpetre came not from I^^di^- " 
was exactly those men whose labours had be^n proscribed 
who could give to France what she wanted. Fourcroy, 
assisted by researches begun by Lavoisier, taught the 
methods of extracting and refining saltpetre ; Guyton de 
Morveau and Berthollet made known a new method of 
manufacturing gimpowder, and studied the makmg of 
iron and steel ; Monge explained the art of castmg and 
borin. cannons of brass for land use, and cast-iron cannons 
for the navy. On the 6th of August 1793 the Conven- 
tion had again to appeal to the Academy in order to know 
what advantage it would be to refine as much as possible 
the coins of the Eepublic ? " In the space of a few years 
science had become a necessity to society at large. In the 
Constitution of the regenerated Academies it was placed at 
the head, as the most important department of knowledge. 



Influence of 

^ Maury, loc. cit, vol. i. p. 329. 
See also Blot's ' Essai sur I'Histoire 
generale des Sciences Pendant la 
Revolution francaise. Pans, IW6. 

2 The last entry in the record ot 
the "proces-verbaux de V Academic 
before the suspension was a Report 
by Borda, Laplace, and Lagrange, 
in answer to a demand of the Con- 
vention, dated 19th January 1/93, 
for advice on the new system of 
weights and measures which the 
Republic should adopt. And so 
necessary had the assistance of men 
of science become to the Govern- 
ment, that even during the suspen- 

sion, which lasted from the 8th 
Au^st 1793 till the 22nd August 
1795, Lakanal had succeeded in 
procuring the following decree from 
the Government of the Convention : 
♦'La Convention nationale decr^te 
que les membres de la ci-Cevant 
Academie des Sciences contmueront 
de s'assembler dans le lieu ordinaire 
de leurs seances, pour s'occuper 
sp^cialement des objets qui leur 
auront ^te ou pourront leur etre 
renvoyes par la Convention natio'i- 
ale" (Maury, loc. cit., p. 331; 
Aucoc, *L'Institut de France, p. 
ccvii, &c.) 

The influence of the first Napoleon on science is natur- 
ally a matter of as much controversy as his merit in «;«^pj^ 
almost every branch of administration. The reports^ on science 

^ According to a decree of the 
Government, dated 13th ventose, an 
X. (4th March 1802), the Institute, 
then consisting of three classes— 
the "Academie des Sciences phy- 
siques et mathematiques," the 
"Academie des Sciences morales 
et politiques," and the "Academie 
de Litt^rature et Beaux -arts"— 
was ordered to furnish " un tableau 
de I'etat et des progr^s des sciences, 
des lettres et des arts, depuis 1789 
jusqu'au V^ vend^miaire an x." 
This "tableau" was to be divided 
into three parts according to the 
three classes of the Institute. These 
Reports were to be repeated every 
five years. The first (and only) 
Reports were not presented before 
February and March 1808. The 
Republican Government had then 
been superseded by the Empire, and 
by a decree of the 3rd pluviose, an 
xi. (23rd January 1803), the Institute 
had been reorganised. There were 
now four classes : 1. Des Sciences 
physiques et mathematiques (corre- 
sponding to the old Academie des 
Sciences). 2. De la langue et de la 
litterature fran9aises (correspond- 
ing to the old Academie frangaise). 
3. D'histoire et de litterature anci- 
enne (corresponding to the " Acad- 
emie d'Inscriptions et de Belles- 
lettres"). 4. Des beaux-arts. " On 
eupprima la classe des sciences 
morales et politiques qui existait 
dans I'organisation du 3 brumaire, 
an iv. Ce fut un trait caracteris- 
tique de la repugnance du premier 
Consul pour la discussion des 
mati^res politiques et leur enseigne- 
ment" (Thibaudeau, ' Le Consulat et 
I'Empire,' Paris, 1835-37, vol. iii. p. 
396). Accordingly there were pre- 
pared four, or rather five, Reports, 
he first in two parts by Delambre 

and Cuvier on the progress of the 
Mathematical and Physical Sciences ; 
the second by Marie-Joseph Chenier 
on the progress of Literature ; the 
third by Dacier on the progress of 
History and Classical Literature ; 
the fourth by Le Breton on Fine 
Arts. Of these the two Reports of 
Delambre and Cuvier gave great 
satisfaction, that of Dacier gave less 
satisfaction ; Chenier, who himself 
admired the eighteenth - century 
philosophy, had an embarrassing task 
to perform, of which, however, he 
acquitted himself worthily (Thibau- 
deau, loc. cit, vol. vi. p. 557). The 
Report of Chdnier has been several 
times reprinted. The new science 
which was founded by Condillac, 
Turgot, Condorcet, and others, and 
which aimed at introducing the truly 
scientific spirit into psychology, psy- 
cho-physical researches, and ques- 
tions of society and legislation, re- 
ceived no recognition, as it had also 
lost its representation in the sus- 
pended ' * Academie des Sciences 
morales et politiques." After the 
re-establishment of this section of 
the Institute in 1832, a royal decree 
of 22nd March 1840 ordered a Re- 
port on the progress of the Moral 
and Political Sciences from 1789 to 
1832. The task was so great that 
it could not be accomplished before 
the Revolution of 1848, and was 
therefore abandoned (Aucoc, ' L'ln- 
stitut de France,' pp. 62 note, 300). 
Some reference to the subject is 
contained in the introduction to 
Chenier's Report, and in the last 
chapter of Dacier's, which was 
written by De Gerando. The true 
history of the new science has been 
recently written by F. Picavet, 
*Les Ideologues,' Paris, 1891. 





which Delambre and Cuvier drew up at his request, 
touching the progress of science during the twenty years 
which followed the outbreak of the Kevolution, have 
become classical as monuments of the achievements of a 
great age,^ and as examples of the best style in which to 
treat such a subject. Written immediately under his eye, 
they cannot be considered quite impartial, so far as the tone 
is concerned in which they refer to his personal favours 
and protection.'^ There can, however, be no doubt that 
he recognised scientific merit, and drew many eminent 
men of science into the service of the Government. The 
institutions on which he prided himself so much, — the 
£cole Normale, the £cole Polytechnique, and the unfin- 
ished scheme of a great centralised Institution of Learn- 
ing and Education, descending from the heights of the 
Institute, through the various branches of the higher and 
secondary into a multitude of primary schools, bearing 
the name of the "University," — had either existed, or 
been planned before him.^ 

^ Napoleon in discussing at the 
council meeting the decree which 
ordered the several reports, said to 
Regnaud : ** Soignez bien cette re- 
daction, car elle sera examinee par 
les pedagogues de toute I'Europe" 
(Thibaudeau, loc. cit., vol. ii. p. 496). 

2 See what Cuvier himself says 
on this subject (Memoires, &c., in 
Flourens, ' Eloges,' vol. iii. p. 187) : 
" Un rapport sur le progr^s des 
Bciences devait etre presente aux 
consuls en fructidor an xi. . . . 
Ou ne fut pret qu'a la fin de 1807 : 
ce n'etait plus aux consuls mais a 
I'empereur que Ton avait a pre- 
senter le travail. II le re^ut avec 
un grand appareil dans la seance du 
conseil d'Etat. M. Delambre et 
moi presentames le notre les pre- 

miers ; le 3 fevr. 1808, accom- 
pagnes de Bougainville, president, 
et des doyens de toutes les sections. 
La ceremonie fut solennelle ; I'em- 
pereur fit une belle reponse, qui 
est imprim^e a la fin du rapport. 
Je sus le lendemain, par M., de 
S^gur et d'autres couseillers d'Etat, 
qu'il avait exprime une grande satis- 
faction de mon rapport en parti- 
culier : ' II m'a loue com me j'aime a 
I'etre, dit-il.' Cependant je m'etais 
borne a I'inviter a imiter Alexan- 
dre et h faire toumer sa puissance 
au profit de I'histoire naturelle." 

* Regarding the University, see 
* Code Universitaire ou Lois, Statuts 
et R^glemens de I'Universite Royale 
de France, mis en ordre par M. 
Ambroise Rendu,' Paris, 1835. In 


It will therefore always remain a matter of doubt to 
what extent he originated ideas, or merely adopted those 
of others before and around him. He favoured the mathe- 
matical sciences, and created great prizes for physical, ^^^^^^ 
notably electrical, discoveries, partly because these pursuits 
promised to surround his Government with glory, partly 
because he recognised their practical importance for the 
purposes of the state and nation ; partly also, because he 
himself had had a mathematical training.^ During his 

the Introduction we read as follows : 
"Bonaparte passait h. Turin. Un 
jour qu'il parcourait le palais de 
I'Universite fondle en 1771 par 
Charles Emmanuel III., il se fit re- 
presenter les statuts qui regissaient 
cette institution. II y vit quelque 
chose de grand et de fort qui le 
frappa. . . . Tout ce plan 
d'education etabli sur la base an- 
tique et imp^rissable de la foi chre- 
tienne, tout cela lui plut, et il en 
garda la m^moire jusqu'au sein de 
ses triomphes en Italie et en AUe- 
magne. Rassasi^ enfin de gloire 
militaire, et songeant aux genera- 
tions futures, apres avoir solidement 
etabli I'administration civile, apres 
avoir releve les autels et promulgue 
le Code Napoleon, apr^s avoir par 
differentes lois, substitu^ les Lycees 
aux Ecoles Centrales, regenere les 
Ecoles de M^decine, et cr^^ les 
Ecoles de Droit, il voulut fonder 
aussi pour la France un syst^me 
entier d'instruction et d'education 
publique. II se souvenait de I'uni- 
versite de Turin et I'agrandissant 
comme tout ce qu'il touchait, dans 
la double proportion de son empire 
et de son genie, il fit I'Universite 

^ Among many references relat- 
ing to this subject, I select one from 
Villemain, * Souvenirs contempor- 
aius d'Histoire et de Litterature,' 
which in the first volume (9™« ed., 

Paris, 1874, p. 137) contains, the 
description of a visit to the Ecole 
Normale in 1812, and a discussion 
with Narbonne, to whom the Em- 
peror had fully expressed his aims 
regarding education and learn- 
ing. "L'Empereur n'est inquiet 
que d'une chose dans le monde, les 
gens qui parlent, et k leur defaut 
les gens qui pensent. ... II 
veut, et il me I'a dit vingt fois, que 
son r^gne soit signale par de grands 
travaux d'esprit, de grands ouv- 
rages litteraires. litre lou^ comme 
inspirateur de la science et des arts, 
etre le chef eclatant d'une epoque 
glorieuse pour I'esprit humain, c'est 
I'idee qui le flatte le plus ; c'est ce 
qu'il a cherchd par des Prix Decen- 
naux. ... II veut (a I'Ecole 
Normale) des etudes f ortement clas- 
siques, I'antiquite et le si^le de 
Louis XIV. ; puis quelques elements 
de sciences mathematiques et plus 
tard la haute geometrie, qui est, 
dit-il, le sublime abstrait, comme la 
grande poesie, la grande eloquence 
est le sublime sensible." Napoleon 
said to Narbonne: "J'aime les 
sciences mathematiques et phy- 
siques ; chacune d'elles, I'algebre, 
la chimie, la botanique, est une 
belle application partielle de I'esprit 
humain ; les lettres, c'est I'esprit 
humain lui-meme. . . . Aussi, 
j'ai deux ambitions : eiever la France 
au plus haut degre de la puissances 





campaigns in Italy and Germany, and on his expeditions 

to Egypt and the East, he surrounded himself with some 

of the greatest scientific authorities, such as Berthollet 

and Monge. From political as well as personal motives, 

88. he discountenanced the once fashionable sensualistic phil- 

SLtXthe osophy. This philosophy has now fallen to the second 

iSl'f ^^^^' ^^^^g^ ^^'^^ represented by eminent thinkers, such 

pSi^^iphy. g^g Cabanis, Destutt de Tracy, Daunou and Garat. It 

was these thinkers of whom Napoleon sneeringly spoke 

under the designation of " Ideologues." ^ 

After all that has been said by admirers to magnify, 
and by opponents to minimise. Napoleon's merits in pro- 
moting the cause of science, and in spreading the modern 
scientific spirit, I cannot but recognise that he was, amongst 
the great heroes and statesmen of his age, the first and 
foremost, if not the only one, who seemed thoroughly to 
realise the part which science was destined to play m 

guerri^re et de la conquete afifermie, 
puis y developper, y exciter tous 
lea travaux de la pens^e sur une 
echelle qu'on n'a pas vue depuis 
Louis XIV. C'etait le but de mes 
Prix Decennaux qu'on m'a gates par 
de petites intrigues d'ideoiogues, et 
de couronnements ridicules, comme 
celui du catechisme de Saint- 

1 A full account of these authors, 
their influence and their aims, will 
be found in F. Picavet, * Les Ideo- 
logues, Essai sur I'histoire des id^es 
et des theories scientifiques, philo- 
Bophiques, religieuees, &c., en France 
depuis 1789,' Paris, 1891. 

Thibaudeau, ' Le Consulat et 
I'Empire,' gives many details re- 
garding Napoleon's connection with 
science, with literature, and with 
the growing industries of France. 
Among the latter see especially 

the great efforts made to supersede 
colonial and foreign goods by home 
productions. Prizes and encourage- 
ments of all sorts were given ; 
technical schools and colleges were 
established ; exhibitions were pro- 
moted. Sheep were imported from 
Spain, sugar was made from raisms 
and beetroot, saltpetre and soda by 
chemical processes, the garance or 
madder root and the Jcermes were to 
take the place of cochenifie ; the pas- 
td the place of the imported indigo. 
That an enormous impetus was 
thus given to chemistry cannot be 
denied. (See Thibaudeau, passim, 
and especially vol. v. p. 248, &c.) 
See also Cuvier's 'Rapport,' &c., 
for an account of applications of 
science, especially chemistry, pp. 
376-386, and Delambre, ' Rapport, 
&c., pp. 326-362. 



the immediate future. This part, as we know, it has 
played both by entirely changing the external face of 
things, and by running out into endless applications ; and 
we have seen the importance of that statistical spirit of 
numbering, measuring, and registering, by which alone 
a survey of complicated phenomena is possible. Of the ^^ J^^^, 
statistical method Napoleon himself made use on an ex- ^J^^e^exten- 
tensive scale : perhaps he was the first among rulers to ^f ^^S'^; 
do so.^ That the great leader of men has to recognise 
not only the inductive philosophy of statistics and aver- 
ages, but likewise governing ideas of a different class. 
Napoleon was well aware, and his ultimate failure may 
be traced to the fact that, however great as a general 
and as a calculator, his soul had no room for those high, 
religious, and unselfish motives of which he himself said 
to Fontanes, that they in the end always decide the fate 
of nations.^ Yet he belongs to the small company of 
great military figures in history — a company which in- 
cludes Alexander the Great, Caesar, and Peter the Great 

^ See Delambre, 'Rapport,' &c., 
p. 222. " Depuis le peu de temps 
qu'on s'en [i.e., with statistics] oc- 
cupe en France, elle y a fait les 
plus grands progr^s, au moyen de 
I'attention particuli^re et des se- 
cours que le Gouvernement francois 
donne h> tous les travaux utiles. 
Les pr^fets des departemens ont ^t^ 
invites a recueillir et k transmettre 
au Ministre de I'int^rieur les 
renseignemens les plus precis sur 
toutes les questions qui sont 
ressort de la statistique." 

2 See ' (Euvres litteraires 
Napoleon Bonaparte,' vol. iii. p. 
Conversation avec Fontanes, Saint 
Cloud, 19 Sept. 1808: "Fontanes, 
savez-vous ce que j 'admire le plus 
dans le monde? C'est I'impuis- 



sance de la force pour organiser 
quelque chose. II n'y a que deux 
puissances dans le monde : le sabre 
et I'esprit. J'entends par I'esprit 
les institutions civiles et religieuses. 
A la longue, le sabre est toujours 
battu par I'esprit." Also vol. iv. 
p. 423 : " Les vraies conquetes, les 
seules qui ne donnent aucun re- 
gret, sont ceux que Ton fait sur 
r ignorance. L' occupation la plus 
honorable comme la plus utile pour 
les nations, c'est de contribuer a 
I'extension des id^s humaines. La 
vraie puissance de la Republique 
fran9aise doit consister desormais 
a ne pas permettre qu'il existe une 
seule id^e nouvelle, qui ne lui ap- 




—who have succeeded in permanently inscribing their 
names in the annals of science beside those of its true 
and great representatives. Some of the glory of Laplace 
and Cuvier falls upon him. Except for this Napoleon has 
ficVoirS; scarcely a place in the history of thought. In it those 
mainly den- ^^^ ^^^^ Kapolcou's scrvauts are rulers and lawgivers; 

it is they who enlighten our century. They were the first 
great exponents of the scientific spirit, nursed under the 
influence of the academic system. This was peculiarly 
a product of the French mind and culture. It is well 
to recall in the words of Cuvier what the scientific spirit 
ia. At the end of the report which he presented in the 
year 1808 he says :^ "These are the principal physical 
discoveries which have lighted up our period, and which 
open the century of Napoleon. \Vhat hopes do they not 
raise! how much does not the general spirit signify, 
which has brought them about, and which promises so 
much more for the future! All those hypotheses, all 
those suppositions, more or less ingenious, which had 
still so much sway in the first half of the last century, 
are now discarded by true men of science : they do not 
even procure for their authors a passing renown. Experi- 
ments alone, experiments that are precise, made with 
weights, measures, and calculation, by comparison of all 
V substances employed and all substances obtained: this 
to-day is the only legitimate way of reasoning and 
demonstration. Thus, though the natural sciences escape 
the appUcation of the calculus, they glory in being subject 
to the mathematical spirit, and by the wise course which 
they have invariably adopted, they do not expose them- 

1 * Rapport, '&c., p. 389. 





selves to the risk of taking a backward step ; all their 
propositions are established with certainty, and become 
so many solid foundations for that which remains to be 
built." ^ 

Nor can we look upon the great prominence which 
Cuvier gives to French names in the course of his survey proSnce 

. , TT given to 

as unjust or partial. He was well aware of the contribu- f^«°^^ 

names by 

tions of other nations : no one has spoken in more gen- ^"^'^^'^' 
erous and correct terms of Priestley and Cavendish, of 
Banks and Eumford, of Pallas, Werner, and Humboldt. 
We must admit the correctness of the remark, "that 
even in those departments where chance has willed that 
Frenchmen should not make the principal discoveries, 
the manner in which they have received, examined, and 
developed them, and followed them out into all their 
consequences, places their names next to those of the 
real inventors, and gives them in many ways the right 
to share in the honour." ^ 

In the first decades of this century the home of the 
scientific spirit was France : for though not born there, 
it was nevertheless there nursed into full growth and 
vigour. But it soon set out on its wanderings through 

^ Compare also the "Reflexions 
sur la marche actuelle des Sci- 
ences," being the introduction to 
the ' Eloges historiques,' vol. i. p. 
1, &c. 

^ 'Rapport,' p. 391. It is also 
remarkable how clearly Cuvier here 
announces the defects which the 
teaching of science was still labour- 
ing under. Whilst he rightly 
praises the great Paris institutions, 
the medical schools, the mathe- 
matical, physical, and polytechnic 
establishments, the new schools of 

technology and agriculture, as un- 
equalled organisations for higher 
instruction, he draws attention to 
the absence of equally efficient ele- 
mentary schools and to the neglect 
of those provincial institutions 
which before that age had already 
done so much to disseminate know- 
ledge and learning. At the end of 
our century both France and Great 
Britain have still only very partially 
supplied the wants which Cuvier bo 
clearly defines in the beginning. 




Other lands and nations. At the end of our century- 
nay, even during the whole of the second half— we find 
this spirit naturalised in Italy, in Germany, in England, 
in the north and east of Europe. There is now no science 
which can be named pre-eminently after one nation. All 
nations have contributed their share to the cosmopolitan 
power and influence which science possesses. They have 
enlarged and deepened the scientific spirit and widened 
its career. Thus far it has been the growth of the 
scientific spirit which has occupied us; we must now 
proceed to study its diffusion, and learn to recognise the 
peculiar features which Germany and England have on 
their part contributed. In doing so, we must turn away 
for a moment from the academic system with which we 
have been specially occupied. 




" No Augustan epoch flowered, 
No Lorenzo favours showered 

Ever German Art upon ; 
She was not by glory nourished 
And her blossom never flourished 

In the rays of Royal sun." ^ 

Perhaps with more correctness Schiller might, early in 
the century, have applied these lines to German science 
than to German art. If art and poetry were only slightly 
indebted to princely protection, German science was still 
less so.^ Leibniz's scientific labours languished while he 

1 Schiller, " Die deutsche Muse." 

2 Astronomy was the only science 
that enjoyed some little princely 
favour. William IV., sumamed 
"the Wise," son of Philip the 
Magnanimous of Hesse and himself 
Elector, was an astronomer of some 
note, and stood in intimate re- 
lations with Mercator, Tycho, and 
other astronomers. In 1561 he 
built himself an observatory at 
Cassel and appointed Rothmann to 
be his " Mathematicus." Frederick 
II. of Denmark gave Tycho a 
magnificent observatory, called 
" Uranienburg," where he laboured 

from 1576 to 1597, but which was 
subsequently destroyed. Tycho 
was then employed by the Emperor 
Rudolf II., and inaugurated the 
observatory in Prague (1599-1601) ; 
he made Kepler his assistant, and 
enabled the latter by the use of his 
observations to find and prove his 
three celebrated laws {" Astronomia 
nova," Prague, 1609 ; " Harmonices 
mundi," Linz, 1619; "Tabulae 
Rudolphinae," 1627). Full details 
will be found in Rudolf Wolf, 
* Geschichte der Astronomic,' Miin- 
Chen, 1877, p. 266, &c. 



of German 

occupied the position of historiographer and diplomatist 
at the Court of Brunswick,^ and Tobias Mayer's valuable 
observations were only published with the aid of English 
money .^ But if the German princes did little or nothing 
directly for the development of science, they indirectly 

1 Leibniz (1646-1716) entered, 
1676, the service of John Frederick, 
Duke of Hanover, as librarian and 
councillor. The Duke died 1679, 
and Ernest Augustus, who in 1692 
was made Elector of Hanover, suc- 
ceeded him. Leibniz's time was 
taken up with diplomatic and legal 
researches and negotiations refer- 
ring to the position of the House 
of Hanover, and the reunion of the 
Protestant and Roman Catholic 
Churches ; latterly with genealogi- 
cal and antiquarian studies refer- 
ring to the history of the House of 
Brunswick. He wrote the ' Annales 
imperii occidentis Brunsvicenses,' 
beginning with the year 768, the 
date of the accession of Charles the 
Great, from whom Leibniz proved 
that the House of Brunswick de- 
scended through the Italian House 
of Este. He carried the history 
down to the year 1005, closing a 
few days before his death with the 
words "quos ex tenebris eruendos 
aliorum diligentise relinquo." The 
work was not printed till 1843, 
when G. H. Pertz, the first editor 
of the celebrated ' Monumenta 
Germanise' founded by the great 
Stein, published it with an elabor- 
ate preface. Of the annoyances to 
which Leibniz was subjected in the 
course of his studies, see an account 
in the correspondence with the 
Minister von Bernstorflf (1705-16), 
published by Doebner, Hanover, 
1882, introduction. See also Guh- 
rauer, * Leibnitz, eine Biographic,' 
2 vols., 2nd ed., Breslau, 1846. 
Considering the greatness of 
Leibniz in so many different 
directions, his motto is note- 

worthy : " Didici in mathematicis 
ingenio, in natura experimentis, in 
legibus divinis humanisque auctori- 
tate, in historia testimoniis niten- 
dum esse ' 

2 Tobias Mayer (1723-62), born 
at Marbach, the birthplace of 
Schiller, from 1751 Professor of 
Economics and Mathematics at 
Gottingen. To use the words of 
Karsten Niebuhr, "Though he 
had never seen a big ship, he 
taught the English how to deter- 
mine the longitude on the open 
sea." He competed for the great 
prize of £20,000 offered in 1713 by 
the Board of Longitude for a method 
of determining the longitude at 
sea within ^° accurately ; smaller 
prizes being offered for an accuracy 
of §° and V. The prize of £5000, 
and subsequently of £10,000, was 
awarded to Harrison in 1758 and 
1764 for his chronometers. Euler 
and Mayer laboured in a different 
direction at the same subject, by 
publishing lunar tables and per- 
fecting the lunar theory. After 
repeated revisions, Mayer sent his 
tables, 1755, to London, where they 
were submitted to Bradley, who re- 
ported favourably on them. After 
further corrections, and after also 
submitting his theory, Mayer's 
widow received, in 1765, £5000, 
Euler £3000, and the work was 
published, 1770, by order of the 
Board of Longitude, under the 
title * Tabulae motuum solis et 
lunse novae et correctai, auctore 
Tob. Mayer : Quibus accedit 
methodus longitudinum promota 
eodem auctore.' 



furthered her cause most powerfully by founding that 
great institution of culture, which more than anything 
else is characteristic of the German mind, in which it 
has found its most perfect expression, and where it can 
be most exhaustively studied — the system of the German 

" There is no people," says Mr James Bryce, " which 
has given so much thought and pains to the development mentofthe 

o ox- X universities 

of its university system as the Germans have done- 
which has profited so much by the services universities 
render — none where they play so large a part in the 
national life." ^ If it is correct to say that this system 
owed its foundation to the German princes, it is equally 
true that its development is the work of the German 
people.^ It may be doubtful whether, without the 



^""^ people. 

^ See James Bryce's preface to 
the English translation of Conrad's 
valuable book, 'The German Uni- 
versities for the last Fifty Years,' 
Glasgow, 1885, p. xiii. 

'^ A great deal has been written 
about the German universities. 
For the purposes of a History of 
Thought, I confine myself to a 
reference to the valuable writings 
of F. Paulsen, * Geschichte des 
gelehrten Unterrichts auf den 
deutschen Schulen und Universi- 
taten,' Leipzig, 1885, and two 
essays in the 45th volume of 
Von Sybel's 'Historische Zeit- 
schrift,' 1881. The succeeding 
phases of mediaeval and modern, 
of Roman Catholic and Protestant, 
of the thought of the Church, the 
Renaissance, the classical and the 
modem ideals, are all reflected in 
the foundation and reform of the 
universities and high schools of 
Germany and the surrounding 
countries. The first foundations, 
in imitation of the universities of 

Paris and of Italy, were Prague 
1348, Vienna 1365, Heidelberg 
1386, Cologne 1388, Erfurt 1392, 
Wiirzburg 1402, Leipsic 1409, 
Rostock 1419. A second epoch — 
under the influence of the human- 
istic studies — begins in the middle 
of the fifteenth century and adds 
eight new foundations — Greifswald 
1456, Freiburg 1457, Trier 1457, 
Basel 1459, Ingolstadt 1472, Tubin- 
gen 1477, Mainz 1477, Wittenberg 
1502, Frankfort on the Oder 1506 
(Paulsen, 'Geschichte,* p. 14). A 
third epoch begins with the Refor- 
mation. The first Protestant uni- 
versity is Marburg, founded by 
Philip of Hesse, 1624. Melanch- 
thon's influence is everywhere deci- 
sive. Tubingen is reconstituted by 
Duke Ulrich 1535 ; Leipsic by Duke 
George 1539. Basel, after three 
years' suspension, is reopened 1532. 
Frankfort on the Oder is reopened 
by Joachim of Brandenburg 1537, 
who also founds the new University 
of Konigsberg 1541. Greifswald is 



individual influence of the former, without the divided 
interests of the dismembered empire, without the con- 
flicting religious views, the political and personal rivalry 
of the many states and sovereigns,^ so many scattered 
centres of culture and learning would have sprung so 
early into existence; but it is not doubtful that it is 
owing to the common interests of the nation, to the 
uniting tie of the same language, the same thought, and 
the same aspirations, that these scattered centres have 
been in course of time united into a great network,^ a 
vast organisation for the higher intellectual work of the 
nation and of mankind. The German nation may pride 
itself on possessing at the present moment the most 

reconstituted on a Protestant foun- 
dation 1539; Rostock in 1540-50; 
Heidelberg by the Elector Frederick 
II. in 1544. Jena is founded 1558 
by John Frederick, Helmstiidt by 
Julius of Brunswick in 1 568 ; Gies- 
sen followed in 1607 ; Riuteln in 
1621 ; Altdorf in 1662. Of the 
greatest influence on German cul- 
ture were the Dutch Protestant uni- 
versities— Ley den 1575, Franeker 
1585, Utrecht 1634, Harderwyk 
1648 ; they were for a long time — 
as formerly the Italian universities 
— the goal of the young scholar's 
wanderings (Paulsen, p. 179). 
They — as well as Geneva — held a 
similar position to the Scotch uni- 
versities (see Sir A. Grant, ' Story 
of the University of Edinburgh,' vol. 
i. pp. 21, 126, 188, 213, 229, 233, 263, 
274, 283, 297, &c., vol. ii. p. 263). 
A fourth epoch begins with the 
foundation of Halle 1694, the first 
really modern university (Paulsen, 
p. 353). The spirit of Bacon and 
Leibniz, represented by Thomasius, 
is the leading power ; it is not by 
any means irreligious, since Francke 

(the so-called "pietist") is as im- 
portant a factor as Thomasius. 
German is substituted for Latin. 
Other universities follow the^ re- 
form, thus Konigsberg 1735, 
Leipsic, Wittenberg, Helmstiidt, 
Kiel, Tubingen, &c. A ffth epoch 
— the evolution of the ideal of 
science in the German sense, Wis- 
sensckaft — begins with the founda- 
tion of Gottingen in 1737. Of this 
more in the text. 

1 Conrad, loc. cit., p. 2 : "There 
is scarcely a stronger bond of con- 
nection between the various parts 
of Germany than that supplied by 
the universities, and in no other 
respect have the barriers that sep- 
arated State from State been so long 
broken down. . . . The historical 
development cannot be accurately 
traced unless the growing extent in 
which the south German universities 
are attended by student* from the 
north be kept in view." 

2 See especially Paulsen's remarks 
referring to the foundation of Got- 
tingen under Georgell. ('Geschichte 
des gelehrten Unterrichts,' p. 425). 


powerful and best equipped army. But this is only the 
creation of the present age. With greater pride it may 
boast of having trained in the course of centuries the 
largest and most efficient intellectual army, ready at any 
moment to take up and carry to a successful issue great 
scientific undertakings demanding the intense thought 
and labour of a few secluded students, or the combined 
efforts of a large number of ready workers. This army 
is scattered through the length and breadth of the land, 
and even beyond its frontiers in neighbouring countries, 
wherever universities and high schools are situated.^ It 
is not a stationary power, but is continually on the move 
from south to north, from west to east, to and fro, exchang- 
ing and recruiting its forces, bringing heterogeneous ele- 
ments into close contact, spreading everywhere the seed 
of new ideas and discoveries, and preparing new land 
for still more extended cultivation. 

^ The extent of the German uni- 
versity system cannot be estimated 
by the twenty universities marked 
on the map attached to the trans- 
lation of Conrad's book, as these 
represent only the existing univer- 
sities of the present German empire ; 
nor yet by the forty-three univer- 
sities given in the appendix, p. 290, 
AS they contain only some of the 
Austrian, but none ot the Swiss 
universities ; nor even by taking up 
Ascherson's valuable ' Deutscher 
Universitats-Kalender,' which con- 
tains the German -speaking univer- 
sities — thirty -four in number in 
1887 — but of course does not con- 
tain the names of those which have 
been suppressed. There are also 
the universities of Denmark, Nor- 
way, and Sweden, which have ex- 
changed many important professors 
with Germany, and those of Hol- 
land in older, of Belgium in modern 

VOL. I. 

times, which have done the same 
thing. The Russian universities 
also were largely organised on Ger- 
man models, though since the re- 
forms of 1863 they aim at a more 
national character. Brandis found- 
ed the University of Athens on 
German lines in 1837. The Russian 
University at Kasan, that "ultima 
musarum Thule," was founded in 
1804, and Gottingen supplied its 
first professors. From there and 
from the hardly less remote Tran- 
sylvanian town, Maros Vdsdrhely, 
there issued the revolution of our 
fundamental notions in geometry, 
and there is reason to believe that 
both Lobachdvsky's and Bolyai's 
theories are ultimately connected 
with the speculations of Gauss. 
See Prof. A. Vasiliev's Address on 
Lobach^vsky, translated by Halsted, 
p. 5 sqq. 



It is not my intention to dwell on the history of the 
German universities, on the gradual growth of the univer- 
sity system ; though every stage in that history is interest- 
ing and important if we wish to understand the inner work- 
ing and usefulness of this great organisation. Neither do 
I wish to do more than just mention, as an equally impor- 
8 tant subject, the geography of the German universities ; 
^'S^bi- how through nearly fifty larger or smaller towns, in the 
Geml^'u^i- course of six centuries, learning and higher education have 
versities. ^^^^ ^^^^^^ ^^^^ ^^^ Germau-spcakiug countries of Europe. 

These figures alone suggest the intricacy of the subject, 
the many springs, the continual ebb and flow of the rising 
tides of ideas, the many courses of thought, the many 
schools of learning, the internal conflicts, the unavoidable 
friction, the healthy competition and rivalry, the repub- 
lican spirit, the impossibility of any creeping stagnation 
of life, the absence of any lengthened tyranny of doctrine, 
of an oppressive hierarchy, or of idols of opinion and 
belief. I leave it to my readers to indulge in comparisons 
easily suggested by these different aspects, to fasten upon 
the strong and upon the weak points of this great system 
of the German universities.^ What I wish to emphasise 


^ The migration of students as 
well as of eminent professors from 
one university to another is one of 
the most important features of 
German academic life. Thus we 
find the imaginative tendencies of 
the southern mtellect represented 
by Hegel and Schelling in philo- 
sophy transplanted into the midst 
of the encyclopaedic and logical 
sciences of the North, or into the 
centre of industrial Switzerland m 
the person of Vischer ; the theo- 
logical criticism of the Tubmgen 
school wandering northward to 

Marburg and Berlin in Zeller ; and 
the philological criticism of Gott- 
fried Herrmann locating itself in 
Zurich in his celebrated pupil and 
biographer Kochly, and in Bavaria 
through Thiersch. Jacobi came from 
the lower Rhine to Munich, where 
also Liebig formed a centre of mod- 
ern scientific celebrities. Savigny 
in Berlin and Thibaud in Heidel- 
berg represent the historical and 
philosophical schools of German 
jurisprudence. Vienna for a long 
time was the most celebrated Ger- 
man training-school of practical 



very strongly here is the existence in the midst of 
European life, all through our century, of this vast organ- 
isation for intellectual work, this great engine of thought ; 
and to assign to it one of the foremost places among the 
great agencies with which we shall have to deal. ' 

The beginning of the present century found this great 4. 

..,.»... Full devel- 

mstitution ot university education in full swing among all opmentof 

o to the German 

the German-speaking nations.^ The eighteenth century syste^'*^ 
brought it to that state of perfection in which we have 
been accustomed to see it. In the course of that century 
it outgrew its earlier and more limited phases of existence, 
its period of more restricted usefulness ; it emancipated 
itself from Court and personal favouritism, from ecclesias- 

;-:t ■; 

medicine and surgery, whereas Ber- 
lin concentrated the great repre- 
sentatives of the more recent scien- 
tific developments. In the course of 
the last hundred years no one uni- 
versity has been allowed to retain 
for any length of time the supremacy 
in any single branch. The light 
has quickly been diffused all over 
the country, when once kindled at 
one point. How will the future 
compare in this respect? 

^ This is not quite the case as 
regards Switzerland. The city of 
Basel, which before the Reformation 
was the seat of much learning, the 
names of Sebastian Brandt, Reuch- 
lin, and Erasmus being intimately 
connected with it, had a university 
from 1459. The antagonism to 
classical and polite literature which 
characterised a large section of the 
Reformers (see Paulsen, p. 128 sqq.) 
destroyed many flourishing centres 
of culture ; amongst them the Uni- 
versity of Basel, which was sus- 
pended in 1529, when the city 
accepted the Reformation, but re- 
opened three years later in 1532. 

Geneva, though this is outside of the 
German-speaking area and presents 
a culture quite peculiar to itself, 
had an academy from 1559, with 
many celebrated professors and 
numerous students of theology from 
all countries of Europe. Lausanne, 
Bern, and Ziirich had colleges or high 
schools in the seventeenth century. 
But down to the nineteenth century 
Basel remained the only university 
in the Continental sense. The 
reasons why Switzerland developed 
her university system so late are 
discussed in Tholuck, *Das akade- 
mische Leben des 17*®" Jahrhun- 
derts,' vol. ii. p. 314, &c., where 
also minute information is given on 
the several high schools of Switzer- 
land. The question is interesting, 
seeing that the greatest in many 
branches of science — such as Ber- 
noulli, Euler, Haller, Cuvier, 
Steiner — have come from Switzer- 
land, and that by reason of the 
names of Rousseau and Pestalozzi it 
has become the centre of modern 
ideas on education. 





The philo- 

The Univer- 
sity of Got- 

tical protection and influence ; it acquired through the 
statutes of governments or special foundations larger and 
better secured means of subsistence ; it substituted the 
vernacular for the Latin tongue. The circle of studies, 
though from early times professedly all-embracing, did 
not become worthily filled up and cultivated with equal 
and impartial care till the fourth faculty, the jp^iloso- 
phical faculty, was properly developed. Theology, law, 
and medicine conduct their studies for practical ends 
and purposes ; the two former especially were frequently 
liable to be used merely for the ends of the Church or the 
State ; but the philosophical faculty embraces all those 
studies which aim at establishing truth, be this defined 
as merely formal or as real, as belonging to method or 
to knowledge. We can assign a definite date to the 
firm establishment of the " libertas philosophandi," and 
the professed introduction of the " libertas docendi " in 
the university programme '—namely, the opening (in 
1734) of the University of Gottingen (inaugurated in 
1737). " The foundation stone," says Professor Paulsen, 
" of the academic constitution is the ' libertas docendi.' 
On this point Von Munchhausen, whom we may call the 
real founder of the university, and his two advisers, 
Mosheim, the theologian of Helmstadt, and Bohmer, the 
jurist of Halle, were agreed. All 4nquisitiones,' so writes 
the former, choke the powers ' ingeniorum,' and spoil the 
beginnings of a learned society. He advises above all 
that the greatest care should be used in the equipment 
of the theological faculty. Accordingly Miinchhausen 
laid his eye upon men whose teaching led neither to 

I Paulsen, •Geschichte des gelehrten Untemchts,' p. 424, &c. 


'Atheismo' nor * Naturalismo,' who neither attack the 
*articulos fundamentales religionis evangelic^,' nor in- 
troduce enthusiasm, nor yet evangelical popedom. Like- 
wise the jurists received full freedom for teaching and 
for the expression of legal opinions, whereas at Halle, 
following the common rule, the Prussian interest, at 
least in matters of public law, was the measure of 
things. At Gottingen the chief stress was laid on 
the culture of the essentially modern sciences. In the 
foremost rank stood the administrative and historico- 
political branches where Putter, Achenbach, Schlozer, 
Gatterer, Heeren, gave to the university her world- 
wide fame ; the mathematical and scientific branches are 
marked by the brilliant names of Haller, Lichtenberg, 
Blumenbach, Kastner; the philological branches by 
Gesner, Heyne, Michaehs. The university met the de- 
mand for encyclopaedic discourses. Miinchhausen ar- 
ranged in 1756 that a member of each faculty should 
deliver a public course on the whole field of the sciences 
taught there ; in the philosophical faculty Gesner treated 
philologico-historical, Kastner physico-mathematical sub- 
jects. An 'Index Lectionum ' of the year 1737 shows 
nine professorships: 1. Politics and Morals. 2. History 
of Literature. 3. History. 4. Elocution and Poetry. 
5. Logic and Metaphysics. 6. Oriental Languages. 7. 
Mathematics and Physics. 8. Administrative Sciences ; 
to which is added, lastly, a professorship of Philosophy 
without special definition."^ 

It is evident that, owing to their constitution, as well 

The original endowment of Got- 
tingen was fixed at 16,000 thalers, 
equal to £2400. This was more 

than double the endowment of 
Halle. (Paulsen, p. 425.) 



as to their number, the German universities were destined 

to become the most powerful organisation for the diffusion 

T. of knowledge. Further, they have been in the course of 

tini?el-s?tfes the prcscut ccuturv more closely linked with many hun- 

and high ^ , . , , • v^ ^i 

schools. ^j.Q^Q of high schools, and with the growmg number ot 
technical schools.^ For both of these they had to train 
the teaching staff, and from the ranks of these they 
again largely filled their own chairs. Thus they not 
only combined in themselves the spirit of research and 
the profession of teaching, but they infused into the 
widely scattered teaching staff of many hundreds of 

^ The technical schools in Ger- 
many and Switzerland are a crea- 
tion of modern times. We can dis- 
tinguish three classes. (1) The 
*'Real8chule." This stands in a 
kind of opposition to the " Latin 
school." The name (according to 
Paulsen, p. 483) occurs first in Halle, 
where the archdeacon Semler es- 
tabUshed in 1706 a mathematical 
and mechanical " Realschule." J. J. 
Hecker established at Berlin in 1739 
an ' ' economico-mathematical Real- 
schule." The object of these schools 
was to teach " Realia," to introduce 
practical rather than learned infor- 
mation. A special development was 
the " philanthropinism " of Base- 
dow, well known even to English 
readers from Lewes's Life of Goethe 
(see vol. i. p. 276, &c.) (2) A 
second class embraces the *' Gewer- 
beschulen," which may be rendered 
*♦ Schools of industry." Karl 
Schmidt ('Geschichte der Piida- 
gogik,' vol. iv. p. 163) calls Beuth 
the founder of them in Prussia, 
1817, and gives the school of 
Aachen as the first. They form 
a kind of bifurcation with the 
higher classes of the Gymnasia (or 
learned schools). They may be 
more specially commercial, agricul- 

tural, or military. (3) Out of these 
a third class — answering to the 
growing demand for the practical 
application of the higher mathe- 
matical sciences — has grown up, 
named polytechnic schools. The 
celebrated Ecole Polytechnique of 
Paris has been the model. The first 
of this class in Germany was estab- 
lished at Vienna in 1816. Then 
followed Munich, Hanover, Karls- 
ruhe, Stuttgart, Niirnberg, Augs- 
burg, Darmstadt, Zurich, Aachen, 
latterly also Berlin (Reichsanstalt) 
and Brunswick (Carolinum). In 
many ways they equal the univer- 
sities in the scientific spirit of their 
teaching. What is wanting is the 
philosophical, the historical, the 
encyclopaedic treatment. In this 
respect they form in their best 
examples a contrast to the Gotting- 
en programme. To many serious- 
thinking minds they indicate the 
gradual dissipation of the German 
ideal of Wissenschaft, the narrowing 
down of Wissenschaft to science in 
the English and French meaning of 
the word. Their danger lies in the 
direction of being contented with 
practical usefulness, as the danger 
of the German type of university lay 
I in being contented with erudition. 


schools the same habit — almost absent in other countries 
— of looking upon private study and research as a 
necessary qualification of the lecturer and teacher. The 
educational organisation of the combined universities and 
higher schools has thus become an equally powerful 
organisation for research, and for increasing knowledge. 
Wherever the progress of learning and science requires 
a large amount of detailed study inspired by a few lead- 
ing ideas, or subservient to some common design and plan, 
the German universities and higher schools supply a well- 
.trained army of workers, standing under the intellectual 
generalship of a few great leading minds. Thus it is s. 
that no nation in modern times has so many schools o/sityaTraln- 
thought and learning as Germany, and none can boast of research. 
having started and carried through such a large number, 
of gigantic enterprises, requiring the co-operation and col- 
lective application of a numerous and well-trained staff.^ 
The university system, in one word, not only teaches 
knowledge, but above all it teaches research. This is 
its pride and the foundation of its fame. 

^ The editions of the ancient 
classics brought out by Tauchnitz, 
Weidmann, and Teubner are well 
known. The collections of the His- 
tories of all countries, begun by 
Heeren and Ukert and continued in 
this century by the publishing firm 
of Salomon Hirzel of Leipsic ; the 
* Jahresberichte,' started by Ber- 
zelius for chemistry, and now separ- 
ately conducted for all the different 
sciences ; contain summaries of the 
labours of the whole world syste- 
matically arranged. There is the 
geographical establishment of Peter- 
mann at Gotha ; not to speak of 
publications specifically national, 
such as the 'Monumenta Germanise,' 

as other countries possess similar 
undertakings. Von Zach was the 
first to establish a regular inter- 
national organ for astronomical 
observations. It was started in 
1798, and soon became the "living 
organ of astronomy," equally ap- 
preciated by Lalande and Gauss. 
This "monthly" was soon succeeded 
by Schumacher's "weekly," the 
' Astronomische Nachrichten.' See 
Wolf, ' Geschichte der Astronomie,' 
p. 764, &c. Humboldt's and 
Gauss's scheme for a network of 
magnetic observations all over the 
world was taken up by English 
men of science. 






The ideal 
of Wissen- 

It is a useful and interesting task to trace intellectual 
developments and habits to their external causes. The 
centralisation of the powers and resources of a whole 
nation into one capital, as was the case in Kome and in 
Paris, may explain the brilliancy of their literatures ; the 
more scattered and diffused culture of Greece and of 
Germany is likewise reflected in their many schools of 
thought and learning ; the insular position of England has 
impressed its advantages and disadvantages upon her 
history, and has influenced her mental life. These influ- 
ences have frequently been pointed out and examhied. 
The historian of thought has another and more difficult 
task to perform. Habits of thought and intellectual 
qualities never become the property of a large number of 
persons unless they assmne a definite form ; through this 
they become a marketable article which can be communi- 
cated and transmitted, and in which those also can par- 
ticipate from whom the deeper motives and higher aims 
remain hidden. Every school has its wsitchword, in which 
its leading thought, its ideal, is embodied. The widely 
scattered and yet closely connected community of intel- 
lectual workers represented by the German university 
system, which covers with its network of universities and 
high schools the German-speaking countries of Europe, 
has during the period of its greatest influence developed 
its own special ideal, and it has expressed this in a special 
word — namely, the word Wissenschaft. Neither the French 
nor the English application of the word science ^ corre- 
sponds to the use or gives the meaning of the word 
WissenscMft This meaning cannot be defined by any 

1 Compare the notes at the beginning of the last chapter, p. 89, &c. 

single word in the English language. Expressions such 
as " student of science " or " science tripos " have a mean- 
ing in English, but they would have none if translated 
into German. In each case the word Wissenschaft would 
require a qualification. An "Academic des Sciences" 
could not according to German usage exist separately 
beside an " Academic frangaise " or an " Academic des 
Inscriptions," for it would include them.^ Scientific 
treatment in England means the exact experimental or 
mathematical treatment of a subject : no one ever calls 
Bentley ^ or Gibbon ^ a great scientific writer, though in 

^ The two older academies in 
Paris, the " Academic des Sciences " 
and the " Academie des Inscriptions 
et Belles Lettres," covered very 
nearly the same ground as the 
modern Berlin " Academie der Wis- 
senschaften und Kiinste," which 
is divided into two classes, the 
" mathematisch - naturwissenschaf t- 
liche" and the *'philo8ophisch-his- 
torische Classe," the two sides 
being equally comprised under the 
term Wissenschaften. A similar 
division exists in the learned so- 
cieties of Vienna, Leipsic, Munich, 
and Gottingen. 

2 Richard Bentley (1662-1742), 
popularly known in England mainly 
through his Boyle Lectures, his 
controversy about the Epistles of 
Phalaris, and his thirty years' feud 
as Master of Trinity College, Cam- 
bridge, with the dons of his col- 
lege, but hardly known "as the 
first, perhaps the only. Englishman 
who can be ranked with the great 
heroes of classical learning" (Mark 
Pattison, *Ency. Brit.'), was from 
the first recognised as a consum- 
mate genius by the scholars of Ger- 
many, by Graevius and Spanheim, 
who welcomed him as "novum 
et lucidum Britanniae sidus," as 
"splendidissimum Britanniae lu- 

men." The many beginnings which 
he had laid for subsequent critical 
research among the ancient classical 
authors were taken up abroad by 
men like Heyne, Reiz, F. A. Wolf, 
Gottfried Hermann, and Friedrich 
Ritschl, in whose hands they have 
developed into a special school of 
philology, counting probably over 
a hundred representatives, many of 
whom have openly avowed their in- 
debtedness to Bentley. (See Kochly, 
* Gottfried Hermann,' Heidelberg, 
1874, pp. 115 sqq., 142, 189. Rib- 
beck, 'Friedr. Wilh. Ritschl,' 2 
vols., Leipzig, 1879 and 1881, vol. 
i. p. 229 ; vol. ii. pp. Ill, 176, &c., 
418, 429.) 

3 Gibbon (1737-94) gave a new 
impetus to the study of the history 
of Roman law through the cele- 
brated 44th chapter of his * Decline 
and Fall of the Roman Empire.' 
It was translated by Professor 
Hugo of Gottingen and Professor 
Wamkonig of Li^ge, and has been 
used as the text- book on Civil Law 
in some of the foreign universities. 
See Smith's edition of Gibbon's 
History with the Notes of Milman 
and Guizot, chap, xliv., note. 
Herder, Savigny, and Niebuhr 
stand all under the immediate in- 
fluence of Gibbon, and Lessing saw 

Has been 
under the 






Germany each stands at the head, and forms the begin- 
ning, of a definite scientific movement. The distinction 
between scientific and philosophical thought which I have 
explained in the Introduction would be unintelligible if 
science were translated simply by Wissenschaft ; the word 
Wissenschaft is not opposed to, but embraces, the word 
philosophy : Fichte, whose whole doctrine was, according 
to French and English ideas, almost the reverse of scien- 
tific, uses the word Wissenschaftslehre to denote and char- 
acterise his system.' In fact the German word for science 
has a much wider meaning than science has in French or 
English; it applies alike to all the studies which are 
cultivated under the roof of "alma mater"; it is an 
idea specially evolved out of the German university 
system, where theology, jurisprudence, medicine, and 
the special philosophical studies are all held to be 
treated "scientifically," and to form together the universal, 
all-embracing edifice of human knowledge.^ Such an 

in him kindred tendencies, though 
in a different direction (see Watten- 
bach, 'Zum Andenkeu Lessing's,' 
p. 23). 

1 Fichte (1762-1814) begins his 
first philosophical work, published 
in 1794, with the words, "Philo- 
sophy is a science," and he then 
proceeds to give to his philosophy 
the term Wissenschaftdehre, or gen- 
eral doctrine or theory of science. 
A further definition which he gives 
is as follows: "A science has a 
systematic form ; all propositions 
in it hang together in one single 
fundamental proposition, and are 
united by it into a whole." It is 
evident that whoever approaclied 
Fichte' 8 writings with the ideal of 
science, as it was established by 
the labours of Lavoisier and the 
great French academicians, would 

not accept these first sentences of 
Fichte 's book. He would admit 
that the sciences as cultivated by 
the great Frenchmen had a unity 
of method, the exact method, the 
method of observation, measure- 
ment, and calculation, but not 
necessarily a unity of system, or 
a highest all-embracing proposition. 
It is evident that science means 
to Fichte something more than it 
meant to the Academie des Sciences : 
it meant Wissenschaft, not merely 
methodical, but systematic, unified 

'^ It would be an interesting task 
to trace in German literature from 
the time of Leibniz the gradual 
evolution of the idea of Wissen- 
schaft, to see how the word has 
grown in pregnancy and signifi- 
cance till it became firmly estab- 


idea, the use of such a term, could only be born and 
developed where the different faculties, the various 
branches of knowledge, lived habitually, for many ages, 
under the same roof, coming into continual contact, and 
learning to regard each other as members of one family, 
as integral parts of one whole. The German university 

lished as denoting a moral as much 
as an intellectual ideal, which it was 
the duty of the German university 
to uphold and to realise. Such an 
investigation would have to show 
how the encyclopaedic view is repre- 
sented by Leibniz, how Winckel mann 
applied the term to the studies 
of antiquity, how Lessing taught 
method and clearness, how Herder 
widened and deepened the view, ex- 
tending it to the elemental forces 
as well as to the finished forms of 
human culture, how it was finally 
raised as the standard of German 
university teaching by F. A. Wolf 
and W. von Humboldt, finding an 
eloquent exposition in Fichte's lec- 
tures on the " Nature of the 
Scholar " (' Vorlesungen iiber das 
Wesen des Gelehrten," Erlangen, 
1805), and a practical realisation 
in the foundation of the University 
of Berlin in 1809, during the period 
of Germany's greatest degradation. 
The following words of Fichte 
have reverberated in the soul of 
many a German scholar to whom 
Fichte's philosophy was unknown 
or distasteful, and this same spirit 
has leavened and united studies 
which stand apparently in no con- 
nection with each other. "The 
scholar" (and specifically the 
teacher of scholars) "shows his 
respect for science [ Wissenschaft^^ 
as such and because it is science, 
for science generally as one and 
the same divine Idea in all the 
various branches and forms in 
which it appears." Of one who 
may be seduced into overestimat- 

ing his own branch, Fichte says : 
" It becomes evident that he has 
never conceived science as One, 
that he has not comprehended his 
own branch as coming out of this 
One, that he thus does not himself 
love his branch as science but only as 
a trade ; this love of a trade may 
otherwise be quite laudable, but in 
science it excludes at once from the 
name of a scholar. ... In the aca- 
demic teacher science is to speak, 
not the teacher himself," he is to 
speak to "his hearers not as his 
hearers but as future servants of 
science," he is to represent the dig- 
nity of science to coming genera- 
tions (Fichte, Werke, vol. vi. p. 
436, &c.) I have myself heard 
expressions similiar to these from 
the mouth of one who represented 
what we should now consider the 
very opposite phase of nineteenth- 
century thought, from one of the 
earliest representatives in Germany 
of exact research, Wilhelm Weber 
of Gottingen. Driven into a corner 
by the ^questionings of devoted 
friends as to his own discoveries 
and contributions, which he was 
modestly fond of tracing to Gauss, 
and unable to deny his own part, 
he would warmly exclaim, "But 
is it not possible that science 
could do something herself ? " Pro- 
fessor Adamson has pointed out 
(* Fichte, 'in "Philos. Clat;sics," p. 
79) how the fundamental idea in 
these writings of Fichte has been 
made familiar to English readers 
through the teaching of England's 
greatest modern moralist, Carlyle. 







system has the merit of having elaborated the widest con- 
ception of science, of having fixed the highest and most 
general scientific standards. Opposed to science is that 
which is unscientific, dilettante, popular; that which is 
not a vocation, but a handicraft ; that which grows and 
lives outside of the great university system, including in 
this the innumerable learned schools which form its base, 
and the academy which forms its summit. 
11. What France and England have elaborated and termed 

andE^g^iand Scicncc, is Called in Germany Exact Science; but it is 

" Science" 

means "Ex- opposcd to the German ideal of science to hold that the 

actScience." ^^ 

exact method is the only method which deserves to be 
called scientific.^ 

^ This is perhaps not quite cor- 
rect. No doubt the term "exact 
Sciences " is used frequently during 
the last half -century to denote 
the mathematical and experimen- 
tal sciences ; very much in the 
same sense as we see them de- 
fined by Cuvier in the beginning 
of the century, and described as 
the ground covered by the labours 
of the "Academie des Sciences." 
There exists, however, in Germany 
another school of thought, very 
intiuential throughout this cen - 
tury, and one that has exerted 
a very wide and wholesome influ- 
ence, which stands in no connec- 
tion whatever with the mathema- 
tical sciences, though it applies the 
word " exact " to its methods and re- 
searches. This is the school which 
maintains that the real introduc- 
tion to the study of antiquity lies 
in a knowledge of the ancient, pre- 
eminently the classical, languages, 
as exact and precise as any mathe- 
matical knowledge could be, and sees 
in an acquisition of such precise 
knowledge the training necessary 
for success in philological and his- 

torical research, just as famili- 
arity with mathematical formula> 
and measuring instruments has long 
been considered quite indispensable 
training to success in the natural 
sciences. Of this view Gottfried 
Hermann may be considered as 
a somewhat one-sided, Friedrich 
Ritschl as a more profound and 
far-seeing, but equally energetic 
representative. It is Ritschl who 
was the most influential. Without 
at present entering into the con- 
troversies which existed between 
what were termed the " Sprach- 
philologen" and the "Sach-philo- 
logen," I desire here to refer to 
the fact that such very different re- 
presentatives of thought as Fichte, 
Weber, and Ritschl, than whom no 
men could be more dissimilar in 
cast of mind, all find their ideal 
expressed in the word Wissenschaft. 
I have quoted Fichte, the specu- 
lative generaliser, and Weber, the 
exact mathematical physicist. I 
will add what Ritschl, the critical 
philologist, says. He trusted, as 
his biographer reports, "in the 
indestructible magnetic force of 

Before the methods of exact science were introduced 
into Germany under English and French influences, the 
Germans possessed many scientific methods. There was 
the science of philosophical criticism, established by 
Kant; the science of historical criticism, of Biblical 
criticism ; the science of philology : all these professed 
to have methods as definite, aims as lofty, and a style 
as pure, as the exact sciences brought with them. 

At present a tendency of thought may exist in Ger- 
many, akin to the positive philosophy in France and 
England, which aims at introducing the methods of the 
natural sciences so as to cover the whole ground of re- 
search, and to allow of no other methods. Should it 
succeed, it will destroy the essential features of the 
German university system, and with it the ideal of 
Wissenschaft as it has existed in all the leading minds 
of Germany during the last hundred years. 

I intend to come back to this subject later on, and 
to define more clearly what the German ideal of science 
— what Wissenschaft — is. That which we are occupied 
with at present is the diffusion of the scientific spirit, in 
the narrower sense, as it was firmly established in France 
through the great mathematicians and scientists at the 

the studies of classical antiquity"; 
he maintained that philology, as 
science, not the barren training of 
■a pedagogic seminary, is the only 
right thing for future masters. 
"The good teacher must, even for 
teaching purposes, have and know, 
both in quantity and quality, more 
than he requires for immediate 
progress ; the portion he requires 
for immediate communication, for 
practical teaching purposes, must 
be delivered out of the fulness and 

the depth of knowledge ; it must, 
even in its circumscribed nature, 
contain the germs of further mental 
development. Such depth, such 
fructifying power, comes only from 
science" {Wissenschaft). See Rib- 
beck, ' Leben Ritschl's,' vol. ii. p. 
277. And as every mode of thought, 
if clearly felt and active, finds its 
expression in language, so Ritschl 
was fond of characterising his scien- 
tific method by the word aKpi^ua. 




of Exact 
Science in 

beginning of this century, as it is summed up in their 
works and in the Memoirs of the Institute. What 
reception did it find in Germany ? How has it thriven 
under the German university system ? These are the 
questions which interest us at present. 

The general recognition of the purely scientific studies 
conducted on a large scale by the French Academy of 
Science, as an integral portion of the German university 
syllabus, belongs to the beginning of the present century. 
During the first forty years of the century complaints 
were continually heard that some of the most important 
sciences were not worthily represented.^ The eighteenth 

^ One of the latest instances of 
such complaint is to be found in 
J. Liebig's paper " On the state of 
Chemistry in Austria" ('Annalen 
der Pharmacie,' 1838, vol. xxv. p. 
339). This was followed by the 
highly interesting pamphlet * On 
the state of Chemistry in Prussia' 
(Braunschweig, 1840). According 
to the eminent author, chemistry 
was the science which was the latest 
to attain a worthy domicile and an 
independent footing in the great 
universities of .Germany. Mathe- 
matical physics had a centre at 
Konigsberg, physiology had been 
established as an independent sci- 
ence at Berlin through the appoint- 
ment of Johannes Miiller in 1833, 
chemistry was still only taught in 
Prussia in connection with other 
branches of science, with medicine, 
with technology, with mineralogy. 
There were no chemical laboratories 
to be found in Prussia. Men like 
Rose, Rammelsberg, Mitscherlich, 
received none or only the scantiest 
support in their practical courses of 
chemistry. It is interesting to note 
how Liebig, whilst pointing to the 
enormous importance which chem- 
istry possesses from an economic 

and political point of view by reason 
of its working great changes and 
revolutions, industrial and other, 
insists on the necessity of teach- 
ing chemistry scientifically, and not 
with an immediate practical bias. 
In this respect he is as much a 
representative of the scientific 
spirit in the wider sense as the 
great men mentioned in the note 
to p. 171. The following passage 
(p. 39) may still be read with in- 
terest and profit : " I have found 
among all who frequent this labora- 
tory [Giesseu] for technical pur- 
poses a prominent inclination to 
occupy themselves with applied 
chemistry. They usually follow 
hesitatingly and with some suspi- 
cion my advice to leave alone all 
this time-absorbing drudgery, and 
simply to become acquainted with 
the necessary ways and means of 
solving purely scientific questions. 
By following this advice their minds 
learn easily and quickly how to find 
the best means ; they themselves 
adapt them to circumstances and 
modify them ; all operations, all 
analyses, which serve to ascertain 
a certain state, which must be 
made in order to find the conditions 


century produced in Germany men of great scientific im- 
portance ; but their position was irregular and uncertain, 
and they undoubtedly do not whoUy or exclusively belong 
to the history of the university system. Leibniz, Euler, 
HaUer, Werner, Markgraf, Tobias Mayer, Lambert, and 
Humboldt are all intimately connected with the growth of 
modern science : their position and sphere of action were 
in each case different.^ Leibniz was a courtier, Euler an 

for the solution of the problem, 
have a definite sense ; each of them 
possesses a certain charm which 
dispels fatigue, and if the question 
IS really answered, then they know 
the ways and means of attaining 
similar ends. I know many who 
are now at the head of soda-, vitriol-, 
sugar-factories, of colour- works and 
other establishments. Without ever 
having had anything to do with them 
beforehand, they were in the first 
half -hour acquainted with the pro- 
cesses, the second already brought 
a number of appropriate improve- 
ments, &c., &c." Similarly Helm- 
holtz in 1862 ('Reden,' vol. i. p. 
142): "He who in the cultivation 
of the sciences aims at immediate 
practical usefulness, may be pretty 
sure that he will miss his aim. 
Science [Wissejischaft] can aspire 
only to a perfect knowledge and 
a complete understanding of the 
sway of physical and mental forces. 
The individual worker must find 
his reward in the joy over new 
discoveries, as new victories of 
mind over matter, in the sesthe- 
tical beauty which an orderly dis- 
play of knowledge affords, &c., &c." 
How little do our modern colleges 
of science correspond with this view 
of Wissenschaft / 

^ On Leibniz (1646-1716), see p. 
158; Werner (1750-1817), p. 118; 
and Tobias Mayer (1723-62), p. 
158. A. von Humboldt (1769-1859) 
is well known to English readers. 

Leonhard Euler (1707-83), a native 
of Basel, passed the greater part of 
his life at St Petersburg as a mem- 
ber oi the Academy, a portion of 
it (1741-66) as an Academician 
at Berlin. He has been termed 
the father of pure mathematics,, 
inasmuch as he freed mathemati- 
cal analysis from geometrical con- 
ceptions, established the notion of 
function or mathematical depend- 
ence, and did much to make the 
theory of numbers an independent 
branch of science. His memoirs- 
are said to number nearly a thou- 
sand ; his works, if all printed,, 
would fill 60 to 80 quartos (see 
Hankel, 'Die Entwicklung der 
Mathematik,' Tiibingeu, 1884, p. 
12). Andreas Sigismund Markgraf 
(1709-82) was born and lived at 
Berlin, a member of the Academy. 
On his various chemical researches^ 
see Kopp, ' Geschichte der Chemie,'" 
voh i. p. 208. Albrecht von Haller 
(1708-77) was a native of Bern. 
He was, next to Leibniz, perhaps 
the most encyclopaedic mind of 
modern times, equally celebrated 
as botanist, physiologist, and poet. 
He has been termed the father of 
physiology. Brought up under the 
celebrated Boerhaave, he accepted 
a chair at the newly founded Uni- 
versity of Gottingen in 1736, and 
taught there for seventeen years 
anatomy, botany, medicine, and 




academician, Werner the head of a great mining school, 
Humboldt a traveller, Markgraf a private gentleman. 
Haller, indeed, shone as a great light in the University 
of Gottingen, where he did more than any other to place 
scientific studies on a level with classical ones, and to 
create for them a permanent abode within the pale of 
"alma mater." He founded in 1751, in close connection 
with the university, the Gottingen Society, which from 
1753 published the celebrated * Gottinger Gelehrte An- 
zeigen/^ Tobias Mayer and Lambert^ can hardly be 
:said to have got much help either from the university, 
,to which the former belonged, or from the Academy, of 
which the latter was a member ; their celebrity rests on 
works produced by private and unaided effort. Hum- 
boldt also depended upon his personal means and upon 
Tiis connection with the Paris Academy, and only attained 
late in life, and in the course of the present century, his 
eminent position as the head and patron of German 
science. Von Zach and Olbers, who together with Tobias 
Mayer and Lambert raised German astronomy during the 
eighteenth century to the level of English and French 
science, stood outside the university system. Von Zach 
was indebted to personal connections, and ultimately 
to Duke Ernest II. of Gotha, for the position which 

1 The 'Gottinger Gelehrte An- 
zeigen' had existed since 1739. 

2 Joh. Heinrich Lambert (1728- 

77), a very extraordinary man, was 
a native of Miihlhausen, Alsace, 
which then belonged to Switzer- 
land. He was received as a mem- 
ber of the Berlin Academy, and 
associated there with Euler and 
Lagrange. He is celebrated through 
his ' Photometry ' (1760) and * Pyro- 
jnetry ' ( 1 7 7 9), his equation referring 

to the orbits of comets, employed 
by Olbers in his method for calcu- 
lating them (Weimar, 1797, re- 
published by Encke, 1847), and his 
prophetic prediction of the proper 
motion of the sun (in his Cosmolo- 
gical Letters, 1761). This motion 
was actually calculated by Sir Wil- 
liam Herschel in his paper " On the 
proper Motion of the Sun and Solar 
System" ('Philos. Trans.,' 1783). 



he held as a kind of corresponding centre of European 
astronomy, and as the leader of a large school of German 
astronomers of this century.^ Olbers was a practising 
physician at Bremen,^ where he followed astronomical 
studies as a recreation, making himself eminent by great 
services to science, among them by his method of calcu- 
lating the orbit of a comet : as the greatest of his services 
he counted the fact of having discovered, trained, and 
appreciated the rising genius of Bessel.^ 

^ Franz Xaver von Zach (1754- 
1832) was a native of Pesth. After 
having served in the Austrian artil- 
lery, and taken to astronomy as a 
favourite study, he spent some time 
in Paris and London, and became 
acquainted with Lalande, Laplace, 
Herschel, Maskelyne, Ramsden, and 
others. He was engaged by Duke 
Ernest II. of Gotha in 1786 to 
erect an observatory on the See- 
berg near Gotha. This was com- 
pleted in 1791. Here he trained a 
number of younger astronomers, 
and was the first to establish and 
maintain a periodical specially de- 
voted to astronomy. It was first 
(1798) published under the title 
* Geographische Ephemeriden,' then 
(1800-13) as 'Monatliche Corres- 
pondenz zur Beforderung der Erd- 
und Himmelskunde. ' Lalande and 
Gauss both testified to the use- 
fulness of this international pub- 
lication, without which Piazzi's 
discovery (see p. 182, note 1) would 
probably have been lost. See 
Wolf, *Gesch. d. Astronomie,' p. 

2 Heinr. Wilh. Mat. Olbers (1758- 
1840) was born near Bremen. He 
followed astronomy as a private 
study. He is mainly known by 
his rediscovery of the first of the 
smaller planets (see p. 182, note 1), 
by his theory, once generally ac- 
cepted, of the origin of the smaller 


planets through the disruption of a 
primitive large planet, and by his 
* Abhandlung liber die leichteste 
und bequemste Methode die Bahn 
eines Cometen aus einigen Beo- 
bachtungen zu berechnen' (1797). 
In this work, by using Lambert's 
equation, he succeeded in perfecting 
the methods of Newton and his suc- 
cessors so as actually to calculate 
the elements of several comets. 
This method is still in general use 
(see Wolf, loc. cit.j p. 519). 

3 Friedr. Wilh. Bessel (1784-1846) 
attracted the attention of Olbers by 
his mathematical abilities whilst em- 
ployed as clerk in a shipping office 
at Bremen. If Tobias Mayer's 
lunar tables were remunerated and 
published with English money, 
Germany repaid the debt by the 
industry of Bessel, who calculated 
and reduced the observations made 
by Bradley (1692-1762, Astronomer 
Royal from 1742) at Greenwich 
during the years 1750 to 1761. 
They had been neglected and re- 
mained unpublished till 1798, when 
Olbers induced Bessel to make 
them useful to science. This he 
did by calculating from them some 
of the most important and funda- 
mental data of astronomy. After 
many years of labour he brought out 
his 'Fundamenta Astronomiae pro 
A. 1755 deducta ex observation- 
ibus viri incomparabilis James 





Science not 
yet domi- 
ciled at the 
German uni- 
during the 

The general impression we receive from a perusal of 
the histories of science and learning in Germany at the 
close of the eighteenth century is, that the university 
system had, so far as philosophical and classical studies 
were concerned, attained almost to the eminence which 
it has held during this century, but that it had not — with 
the exception perhaps of Gottingen — received into its pale 
the modem spirit of exact research, such as it had been 
developed by the great French Academicians. Eminent 
students of science lived outside of the universities, belong- 
ing wholly or largely to the international Eepublic which 
had its centre in Paris, exerting little influence on higher 
German education through the universities, and hardly 
any on German literature, which had meanwhile ripened 
into the age of Classicism. This scattered condition of 
German science gave it on the one side a character 
which was foreign to the general tendencies of German 
thought, since this had come under the excessive in- 
fluence of the speculative spirit without that whole- 
some check which exact research has always exerted.^ 

Bradley in specula astronomica 
Grenovisensi per A. 1750-62 insti- 
tutis ' (1818). By his determina- 
tion (1838-40) of the parallax of the 
star 61 Cygni he made the first ac- 
curate calculation of the distance of 
a fixed star, which he computed at 
12 billion astronomical miles. 

^ It was the age of the Natur- 
philosophies which, through the in- 
fluence of Schelling in the south 
and Hegel in the north of Ger- 
many, filled the chairs in the uni- 
versities, and penetrated into the 
learned societies. This philoso- 
phy of nature had the effect of 
frequently replacing induction by 
speculation, the patient work of 

the calculator, the observer, the 
experimenter, and the dissector by 
general theories, such as, applied 
to literary, historical, and poetical 
subjects, had acquired a certain 
importance, and a semblance of 
veracity and usefulness. In France 
the whole spirit of the Academy of 
Sciences opposed this form of learn- 
ing. Cuvier denounced it or re- 
garded it with suspicion, in Eng- 
land it remained unknown, and in 
Germany itself individual great 
minds opposed it, or did their 
work outside of its influence. 
Such were notably A. von Hum- 
boldt and Gauss. Younger men, 
such as Liebig and Joh. Midler, 


On the other side, we find in the wide domain of gen- 
eral literature valuable beginnings and foreshado wings 
of later scientific thought, as in Georg Forster ^ and in 

came temporarily under its influ- 
ence. As regards its harmful 
effect on the natural and medical 
sciences, the popular addresses of 
Helmholtz and Du Bois-Reymond 
may be consulted. Its philoso- 
phical value will frequently oc- 
cupy us in later chapters of this 
work. Its period can be approxi- 
mately fixed by the publication in 
1797 of Schelling's 'Ideen zu einer 
Philosophie der Natur.' The death 
of Hegel in 1831, and Humboldt's 
Berlin lectures during the years 
1827 and 1828, may be considered 
as marking approximately the end 
of the generation which came 
under the one-sided influence of 
the Naturphilosophie. We shall 
have ample occasion later on to 
notice how many valuable leading 
ideas connected with this phase 
of thought were temporarily aban- 
doned and have since come promi- 
nently before the scientific world. 
The year 1830 marked the victory 
of Cuvier's ideas over those of his 
great contemporary Geoffroy St- 
Hilaire in the French Academy, 
and with it the temporary defeat 
of the valuable suggestions con- 
tained in the writings of Lamarck 
and Goethe. 

1 Georg Forster (1753-94) was one 
of those unique men in the history 
of literature and science who com- 
bine the artistic with the scientific 
spirit, promoting equally the inter- 
ests of poetry and of exact know- 
ledge by a loving study of Nature, 
leading to new views of art as well 
as to deeper conceptions in science. 
He may be classed with White of 
Selborne and other naturalists of 
England among the small number 
of those who quietly and unostenta- 
tiously prepared the healthier forms 

of Naturalism which permeate the 
poetical and scientific thought of our 
century, culminating in the great 
names of Wordsworth and Goethe, 
of Humboldt and Darwin, of Wal- 
lace and Haeckel. His life presented 
many interesting and some un- 
happy episodes; it introduces us 
into the political aspirations of 
the early French Revolution, to 
which he sacrificed himself. It 
has been written by Moleschott, the 
naturalist, by Heinrich Konig, the 
novelist (* G. Forster in Haus und 
Welt,' Leipzig, 1858, 2 vols.), by 
Klein ('Georg Forster in Mainz'). 
Fr. Schlegel (' Charakteristiken und 
Kritiken,' vol. i.), Gervinus (Intro- 
duction to the 7th vol. of 'Georg 
Forster's Werke '), and Hettner 
(' Literatur des 18*6" Jahrhunderts,* 
vol. iii.) have written appreciative 
essays on him. A. von Humboldt 
calls him his master (* Kosmos,* 
vol. i. p. 345), and Herder (Pre- 
face to Georg Forster's translation 
of ' Sakuntala ') prophesies his last- 
ing fame against the opinion of 
his less appreciative contempor- 
aries. He has a place in the class- 
ical literature both of England and 
Germany through his beautiful de- 
scription of Captain Cook's second 
voyage round the world — his 
father, Joh. Reinhold Forster, hav- 
ing been selected as the naturalist 
on that voyage (London, 1777, 2 
vols. 4to), German edition, 1779. 
Richard Garnett has said of him : 
"His account of Cook's voyage is 
almost the first example of the 
glowing yet faithful description of 
natural phenomena which has since 
made a knowledge of them the 
common property of the educated 
world. ... As an author he stands 
very high ; he is almost the first 






Goethe ; ^ but they could hardly be encouraged and de- 
veloped sufficiently without that strict training which is 
acquired through the routine of the class-room, or under 
the eye of a recognised authority. 

The want of academic union and organisation, and the 
?^riSis. scattered situation of the many small centres of learning 
and culture in Germany, led, however, to the early de- 
velopment of those scientific periodicals which form such 
a characteristic feature in German literature. They were 
the medium for the exchange of ideas, and the collecting- 
ground for researches, in an age when exact science was 
not systematically taught at the Universities, and when 
such researches otherwise would have run the risk of 
being lost in obscurity or oblivion. 

At the end of the eighteenth century Germany, 

and almost the best of that valu- 
able class of wi-iters who have made 
science and art familiar by repre- 
senting them in their essential 
spirit, unencumbered with techni- 
cal details" ('Ency. Brit.,' vol. ix. 
p. 419). Forster lived in the period 
of transition from the thought of 
the eighteenth century to that of 
the nineteenth, and a study of his 
Life, Works, and Correspondence is 
a very good introduction to nearly 
all the great problems which then, 
especially on the Continent, trou- 
bled the minds of the greatest men. 
If he may be accused of want of 
patriotism, he is certainly to be 
admired for his freedom from na- 
tional narrow-mindedness. 

1 It has taken nearly a century 
before the real value of Goethe's 
scientific ideas has been correctly 
gauged. His non- academic sur- 
roundings, his unscientific style, his 
antagonism to Newton, his mission 
as a poet — supposed in those days 
to be less realistic than we have 

since become accustomed to con- 
sider it — all these circumstances 
contributed to the result that 
Goethe's scientific writings were 
not taken au sirieux by the natural- 
ists of his age. Then came a period 
when men of science began to sift 
the wheat from the chaff ; but even 
they have only tardily recognised 
that, more than in special dis- 
coveries or suggestions, his great- 
ness lies in that general conception 
of Nature which was so foreign to 
his age, and which nevertheless is 
becoming more and more familiar 
and necessary to ours. See espe- 
cially Helmholtz's valuable essays 
on Goethe as naturalist from the 
years 1853 and 1892 ('Vortriige,' 
vol. i., and address delivered at the 
meeting of the Goethe Society at 
Weimar, 1892), and the remark- 
able progress of his own views on 
this subject contained therein. We 
shall have ample opportunity of re- 
verting to this subject. 

( ^ Carl Friedrich Gauss (1777- 
1855), a native of Brunswick, called 
by Laplace the first mathematician 
of Europe, may be considered as 
the first and foremost representa- 
tive of the modern mathematical 
school, of which we shall have to 
treat later on. Unlike most of 
the great mathematicians of the 
Continent, he was self-taught, and 
followed in his earliest works quite 
independent lines of thought; re- 
sembling in this the great isolated 
thinkers of Britain whose ideas take 
a generation or more to penetrate 
into the text-books of the school. 
Gauss had the highest opinion of 
the dignity of pure science, and it 
almost appears as if, among the 
modems, only Newton had come 
up to his ideal. For him alone 
he reserves the adjective "sum- 
mus," and he adopts his synthetic 
and classical methods of exposition, 
removing, as has been said, the 
scaffoldings by the aid of which he 
had erected his monumental works. 

Gauss trained few mathematicians ; 
but among the few who penetrated 
the secret of his ideas are such 
original thinkers as the Hungarian 
Bolyai (1775-1856), the geometers 
Mobius (1790-1868) and Von Staudt 
(1798-1867), who all mark quite 
independent lines of research. On 
Gauss see Sartorius, 'Gauss zum 
Gedachtniss,' Leipzig, 1856 ; Han- 
selmann, *K. F. Gauss,' Leipzig, 
1878; E. Schering, *C. F. Gauss,' 
Gottingen, 1887. 

2 It appears that Gauss, to whom 
the arithmetical discoveries of Fer- 
mat and the proofs of Euler, La- 
grange, and Legendre remained for 
a long time unknown (see his Works, 
edited by Schering, vol. i. p. 6; 
vol. ii. p. 444), had independently, 
in his eighteenth year, as a student 
at Gottingen, already arrived at a 
great number of propositions refer- 
ring to the properties of numbers, 
and had then also found methods 
of geometrically constructing the 
regular polygon of seventeen sides. 



though not by its universities, was already an import- 
ant power in the Eepublic of exact science which 
then had its centre in Paris. Just at the beginning 
of the nineteenth century two events happened which 
foreboded for the highest branches of the mathematical 
sciences a revival of the glory which in this depart- 
ment Kepler and Leibniz had already given to their 
country. These two events are both coupled with the 
name of Carl Friedrich Gauss. They added greatly 
to the reputation of the University of Gottingen, with 
which this remarkable man was connected for half a 
century.^ The first was the publication of the 'Dis- 
quisitiones Arithmeticae ' in Latin in 1801 — a work by 
which Gauss placed himself on a level with the great 
mathematicians, Euler, Lagrange, and Legendre.^ The 


ical re- 







second was the invention of a new and shorter method 
of calculating the orbit of a planet from a limited number 
of contiguous observations/ This method was communi- 

The latter was the first addition 
made after 2000 years to the 
knowledge of this matter possess- 
ed by the ancients. (See ' Disquis. 
Arithm.,' sec. 365: *' Magnopere 
sane est rairandum, quod, quum 
jam Euclidis temporibus circuli 
divisibilitas geometrica in tres et 
quinque partes uota fuerit, nihil 
his inventis intervallo 2000 anno- 
rum adjectum sit," &c. ; and his 
manuscript note to this passage, 
given by Schering, vol. i. p. 176 : 
'* Circulum in 17 partes divisibilem 
esse geometrice, deteximus 1796, 
Mart. 30.") It is probably owing 
to the independent manner in which 
Gauss approached the subject that 
he early found the necessity of 
treating subjects of higher arith- 
metic (i.e., of the theory of num- 
bers or "discrete magnitudes" as 
distinguished from algebra, which 
is the theory of "continuous mag- 
nitudes") by an independent me- 
thod, for which he invented a 
language and an algorithm. He 
thus raised this part of mathe- 
matics into an independent science, 
on which the ' Disquisitiones Arith- 
meticae ' is the first elaborate and 
systematic treatise. Legendre's 
'Traite des nombres' (1799) is a 
complete thesaurus of all that was 
at that time known and of what 
was added by him, but it does not 
attempt to establish the science on 
a new basis. 

^ On the 1st January 1801 
Piazzi at Palermo had found a 
movable star of 8th magnitude, 
RA. 57" 47', ND. 16" 8', which he 
announced to Bode at Berlin as a 
comet on the 24th January ; but 
a few days later he concluded it 
must be a planet, and named it 
** Ceres Ferdinandea." No one be- 

sides Piazzi could find the star, but 
several astronomers, Piazzi himself, 
Olbers at Bremen, and Burckhardt 
at Paris, tried to calculate the orbit 
from the observations of the dis- 
coverer, which were contained 
within only 9 degrees. The at- 
tempt to do so under the sup- 
position of either a circular or a 
parabolic or an elliptic orbit failed, 
and Olbers expressed the fear that 
with the circular or elliptic ele- 
ments which had been published in 
Zach's periodical, it might prove 
impossible to find the star when 
it should again become visible. 
Very near the expected time, as 
i late as the beginning of December, 
Gauss communicated his elements 
to Von Zach, who published them 
at once, recommending astronomers 
to follow Dr Gauss's figures and 
look 6" to 7° more eastward than 
the positions of Burckhardt, Piazzi, 
and Olbers indicated. And actu- 
ally on the 7th December 1801 
Zach himself, and on the 1st Janu- 
ary 1802 Olbers, succeeded in find- 
ing the star, "like a grain of sand 
on the sea -shore," very near the 
positions calculated by Gauss. 
These results, followed soon by 
the discovery of other planets by 
Olbers and Harding, gave a great 
impetus to the study of astronomy. 
Gauss's methods were published 
in extenso in the now celebrated 
* Theoria motus corporum coeles- 
tium ' in 1809. Two problems are 
herein treated in a novel and com- 
plete manner. The first was to 
calculate by a simple and accurate 
method from the necessary number 
of observations the orbit of a planet 
or comet on the assumption of New- 
ton's law of gravitation, but with- 
out any other special conditions. 




cated to Von Zach in the course of the year 1801, and 
enabled him and Olbers to rediscover the first of the 
small planets, Ceres, which Piazzi had observed on the 
1st of January 1801 at Palermo, and afterwards lost as 
it approached the region of the sun's light. Through 
this Gauss placed himself on a level with the great 
French astronomers Laplace, Lalande, and others. The 
new professor of mathematics and director of the obser- 
vatory of Gottingen was admitted into the august com- 
pany of the Paris academicians, who then ruled, and since 
the death of Euler had almost monopolised, the mathe- 
matical studies of the world. Although Gauss thus 
introduced the higher and abstract branches of exact 
science into the programme of a German university, 
and established a link between Paris and Germany 
in mathematics, as Humboldt had done shortly before 
in the natural sciences, fully a quarter of a century 
was to elapse before the spirit of exact research, and le. 
of the higher mathematics, really began to leaven the spint enters 

the univer- 

German universities. It then at length entered the field cities ih the 

*-• second quar- 

as a third and equally important agent by the side of the ^^^°^t^® 


This was achieved to perfection, 
a proof of the usefulness of the 
method being the fact that Gauss 
succeeded in finishing in one hour 
a calculation which had taken Euler 
three days, and had resulted in his 
blindness. The second problem 
arises from the fact that the num- 
ber of observations is always in 
excess of the number mathemati- 
cally necessary, and that, owing to 
the unavoidable inaccuracies, dif- 
ferent sets of observations give 
filightly difierent orbits. How are 
these to be used so as to give the 

I most correct average result ? This 
i involves a question in probabilities. 
I As early as 1795 Gauss was in pos- 
i session of the so-called method of 
I least squares, which occurred to him 
so naturally that he suspected that 
Tobias Mayer must have already 
known about it. It also occurred 
independently to Legendre, who 
was the first to publish it, in 1806, 
in his ' Nouvelles methodes pour la 
determination des orbites des co- ^ 
mdtes. ' See Sartorius, * Gauss zum ) 
Gediichtniss, ' p. 41 sqq. 







philosophical and classical spirit. During these twenty- 
five years Gauss lived and soared in solitary height — a 
name only to the German student, as Euler had been 
before him. Probably he was better known to the 
younger astronomers whom he trained, and the elder ones 
with whom he corresponded. But astronomy was not 
then within the pale of the universities. To what extent 
the character of Gauss's own genius was the cause of this 
it is difficult to say.^ He himself had not come under 
the influence of any great teachers such as Paris then 
possessed; he was self-taught, and had early imbibed 
a great admiration for the methods of Euclid, Archimedes, 
and Newton ; he wrote in the classical style fitted for all 
times, but not for uninitiated beginners.^ It is certain. 

^ Bjerknes, in his most interesting 
memoir on Abel, refers frequently 
to the awe in which Gauss was held 
by younger mathematicians. 

2 In this Gauss resembled New- 
ton. He was therefore, like Newton, 
frequently forestalled by others, 
who published his new methods 
and ideas in an unfinished and frag- 
mentar}' form; whereby it is not 
suggested that these simultaneous 
discoveries or inventions were not 
quite independent. Two examples 
of this may be added to those given 
above. When Gauss published the 
*Disquis. Arith.' in 1801, he left 
out the last or eighth section, which 
was to treat of the residues of the 
higher orders. He had already 
nearly completed the theory of 
biquadratic residues. In dealing 
with this subject he had found it 
necessary to extend the conception 
of number beyond the limits then 
in use. If we confine ourselves to 
integers, the only extension which 
then existed of the notion of number 
was in the use of negative numbers. 

These were counted on a straight 
line backward, as positive (or or- 
dinary) numbers were counted for- 
ward. Gauss conceived the idea of 
counting numbers lat/ Uy from the 
straight line which represented the 
ordinary — positive and negative — 
numbers. He called numbers which 
were thus located in the plane 
" complex numbers," as they had to- 
be counted by the use of two units, 
the ordinary unit 1 and a new unit 
i. He also showed that this new 
unit i stood in such relations to the 
ordinary unit 1 as were algebraically 
defined by the mysterious imagin- 
ary symbol ^J-1. The complete 
exposition of this new or complex 
system of counting was not ex- 
plained by Gauss till the year 
1831, when he published the 
' Theoria residuorum biquadrati- 
corum.' In the meantime the 
geometrical representation of im- 
aginary quantities had been devised 
and published by Argand (1806), 
but not being employed for such 
important researches, it had re- 




however, that the spirit of exact and specially mathe- 
matical research owed its right of domicile within the 
universities to others who came after him, and to cir- 
cumstances with which he was hardly connected. 

The man to whom Germany owes its first great school 
of mathematicians was Jacobi. He was self-taught like ^^^^^^; 
Gauss; but whilst Gauss followed in the footsteps of 
Newton and the ancients, Jacobi followed in those of 
Euler, Lagrange, and Laplace. The style and methods 
of these mathematicians, being more suited for didactic 
purposes than the classical style of Euclid, Newton, and 
Gauss, was probably more congenial to the mind of 
Jacobi, who from his twenty-first year (1825) developed 
a great activity as an academic teacher.^ He was first 


mained unknown and unnoticed. 
See on the history of the subject, 
Hankel, 'Theorie der complexen 
Zahlensysteme,' 1867, pp. 71, 82. 
Gauss, through hiding his researches 
on this subject so long, lost the 
claim to the priority of the inven- 
tion, though not of the effectual 
use of it. In another instance he 
allowed others to appropriate the 
merit of cultivating a large new 
field which had been familiar to 
him many years before. It was 
known all through the first half of 
the century that Gauss was in pos- 
session of valuable discoveries in 
what he termed the " new transcen- 
dent functions. " References in the 
' Disquisitiones,' § 335, in his corres- 
pondence with Schumacher, Bessel, 
Gibers, and Crelle, had made his 
friends curious to see the " amplum 
opus" which he had promised. It 
appears, however, that, independ- 
ently of him, Jacobi and Abel 
(1802-29) following the investiga- 
tions of Legendre (whose labours 
began in 1786 and culminated in 

his great work * Traite des fonctions 
elliptiques, &c.,' 1825-28, 2 vols, 
and 3 supplements), succeeded in 
developing the theory very much 
on the same lines as Gauss had 
taken nearly a generation earlier. 
Eminent mathematicians who, since- 
the publication of Gauss's posthu- 
mous papers, have fully investi- 
gated the subject, assign to Jacobi 
and Abel the undisputed priority 
of publishing, but to Gauss that of 
discovering, the fundamental pro- 
perties of the "doubly periodical" 
functions. Full details will be 
found in the historical introduction 
to Enneper's ' Elliptische Func- 
tionen,' 2nd ed., Halle, 1890. See 
also Gauss's Werke, vol. iii. p. 491- 
496 ; Dirichlet's Discourse on Jacobi 
in Jacobi's Werke, vol. i. p. 11 ; C. 
A. Bjerknes, ' N. H. Abel,' Paris, 
1885; Koenigsberger, 'Zur Ges- 
chichte der Theorie der elliptischen 
Transcendenten,' Leipzig, 1879. 

1 Carl Gustav Jacob Jacobi (bom 
at Potsdam 1804, died at Berlin 
1851) was the first great mathe- 






at Berlin, then at Konigsberg; these two universities 
havincr become through him and Bessel the German 
teaching centres of the higher mathematics, both pure 
and applied. They have up to the present day fully 
maintained this pre-eminent position. They were teach- 
incr centres in the sense defined above — not only as 
regards mathematical knowledge and method, but like- 
wise as regards mathematical research. For this pur- 
pose — as in the philological sciences — the lecture-room 
was not sufficient ; there was also wanted a repository 
for the independent and original contributions of the 
school. Like the ficole polytechnique thirty years before 
in Paris, the Berlin school of mathematicians started with 
an > important periodical. This was known as Crelle's 
Journal. Together with the Memoirs of the Paris Aca- 
demy and the Journal de TEcole polytechnique, it forms 
the principal repository for the higher mathematical work 
of the first half of the century.^ It was also through 

matical teacher of Germany. Of 
him Lejeune Dirichlet says : '* It 
was not his business to communicate 
what was finished and what had 
been communicated before ; his 
lectures all treated of subjects 
which lay outside of the field of 
the text-books, and covered only 
those parts of science in which he 
had himself been creative. With 
him this meant that they exhibited 
the greatest variety. His lectures 
were not remarkable for that kind 
of clearness which is character- 
istic of intellectual poverty, but for 
a clearness of a higher kind. He 
tried primarily to show the leading 
ideas which underlay any theory, 
and whilst he removed everything 
that had an artificial appearance, 
the solution of problems presented 
itself so easily to his hearers that 

they could hope to do something 
similar. . . . The success of this 
unusual method was truly remark- 
able. If in Germany the knowledge 
of the methods of analysis is now 
spread to a degree unknown to 
former times, if numerous mathe- 
maticians extend the science in 
every direction, this gratifying re- 
sult is principally owing to Jacobi. 
Nearly all have been his pupils," 
&c. (Dirichlet's Discourse in the 
Academy of Berlin, 1852, Jacobi's 
Werke, vol. i. p. 21.) 

^ The two mathematicians on 
whom A. L. Crelle (1780-1855) re- 
lied mainly for contributions when 
he started the ' Journal fiir die 
reine und angewaudte Mathematik ' 
in 1826 were Abel and Steiner. 
For originality of thought they 
stand quite alone. Both extended 

^■fimrttli -- 


Jacobi, and still more through his contemporary Lejeune 
Dirichlet (born 1804 at Duren, of French extraction, 
and trained in Paris under Laplace, Legendre, Fourier, 

the field of research which they 
cultivated by fundamentally new 
ideas of such breadth that fully 
half a century was required be- 
fore they were thoroughly appreci- 
ated by mathematicians. Abel 
(a Norwegian by birth) died in 
1829 when only twenty -seven 
years old, having during the four 
years which embrace his published 
memoirs extended the limits of 
algebra and laid the foundations 
for a more comprehensive treat- 
ment of the higher or transcendent 
functions, or forms of mathematical 
dependence. Mathematicians be- 
fore him had tried to solve algebra- 
ically equations beyond the fourth 
degree, but had failed. Abel proved 
that the problem as then conceived 
could not be generally solved. Le- 
gendre had through his unaided 
labours, extending over thirty 
years, established the theory of 
elliptic integrals as far as w^as 
possible on the lines then adopted. 
Abel — and simultaneously Jacobi — 
treated the subject from an entirely 
novel point of view, and by doing 
so opened out quite a new field of 
research, the extent and importance 
of which Abel fully recognised when 
he presented to the French Acad- 
emy his memoir of 1826, in which 
he dealt with functions of which 
those studied by Legendre and 
Jacobi were only special cases. 
This memoir, containing Abel's 
celebrated theorem, which he had 
already discovered in 1825, and 
which was published in a brief ar- 
ticle in Crelle's Journal in 1829, re- 
mained unnoticed, being, as Legen- 
dre explained to Jacobi, almost un- 
readable. SeeEnneper, 'Elliptische 
Functionen,' 2nd ed., p. 192; Jaco- 
bi's Werke, vol. i. p. 439, &c. Abel 

has been called the greatest mathe- 
matical genius that has yet existed 
(Oltramare in ' La grande Encyclo- 
pe'die,' art. ''Abel"); his fellow- 
worker, Jacob Steiner (1796-1863, 
a Swiss by birth), has been termed 
the greatest geometrician of modern 
times. The progress of analysis 
had thrown into the background 
purely geometrical researches, al- 
though a revival of these had com- 
menced in France with Monge and 
his followers, and had been further 
pronioted by Poucelet, as well 
as simultaneously by Mobius and 
Pliicker in Germany. The labours 
of the two latter remained for a 
long time unknown and unrecog- 
nised. Steiner, who was self- 
taught, who disliked the calculus, 
and considered it a disgrace that 
geometry could not solve her prob- 
lems by purely geometrical methods, 
undertook to find the common root 
and leading principle which con- 
nected all the theorems and por- 
isms bequeathed to us by ancient 
and modern geometry ; he brings 
order into the chaos, and shows 
how nature with a few elements 
and the greatest economy succeeds 
in giving to figures in space their 
numberless properties. He not 
only completed that part of geome- 
try which had been treated by the 
ancients — the geometry of the line, 
the conic sections or curves of the 
second order, and the surfaces in 
space corresponding to them— but 
he also attacked problems which 
before him had been solved only by 
the calculus, and even succeeded in 
carrying his methods beyond the 
reach of the calculus of varia- 
tions, specially invented to deal 
with geometrical questions. Like 
Fermat in the theory of numbers, 


I fa 







in 1826 



Poisson, Cauchy), that the great work of- Gauss on the 
theory of numbers, which for twenty years had remained 
sealed with seven seals, was drawn into current mathe- 
matical literature, and became, as Newton's ' Principia ' 
had become a century earlier, an inexhaustible mine of 
wealth for succeeding generations. 

About the same time the experimental side of exact 
research — the use of the chemical balance, through which 
Lavoisier and his followers had done so much to establish 
chemistry on a firm and independent basis — received a 
great impetus by the establishment of the first chemical 
laboratories within the pale of the universities.^ In this 
direction the greatest influence probably belongs to the 
small town of Giessen, where Liebig opened his cele- 
brated laboratory in the year 1826. It became the 

Steiner in geometry left to his fol- 
lowers a large number of theorems 
and problems without proofs which 
he had solved by his methods ; and 
it was only in quite recent times 
that the Italian Cremona succeed- 
ed in definitely clearing up the 
whole of this original and valuable 
bequest. See Hankel, 'Die Ele- 
mente der projectivischen Geome- 
tric, chapter i. ; Jacob Steiner, 
Werke, vol. ii. p. 495. 

1 On Liebig's laboratory see Hof- 
mann's Faraday Lecture, p. 8. 
Chemical laboratories existed for 
teaching purposes before Liebig's 
at Giessen. Kopp (' Geschichte der 
Chemie,' vol. ii. p. 19) mentions one 
at Altorf, which was founded, 1683, 
by the council of the city of Niirn- 
berg for academic teaching pur- 
poses. For the training of the 
modern school of chemists no man 
did more than Berzelius, in whose 
laboratory there were trained Chr. 
Gmelin, Mitscherlich, H. and G. 

Rose, Wohler, Magnus, Arfvedson, 
Nordenskiold, Mosander, and others. 
Sir William Thomson (Lord Kelvin) 
in ' Nature,' vol. xxxi. p. 409, men- 
tions the beginnings of laboratory- 
teaching at Glasgow by Prof. 
Thomas Thomson in 1828. But 
what was probably peculiar to 
Liebig's laboratory was the syste- 
matic and methodical training, on 
a specially devised plan, in quali- 
tative, quantitative, and organic 
analysis, by which young persons 
were introduced to a thorough 
knowledge of chemical properties 
and manipulations. The guides, 
text-books, and tables for analytic 
work of Will, Fresenius, and others 
were elaborated to meet the 
requirements of such methodical 
teaching. Almost simultaneously 
with Liebig at Giessen, Purkinje at 
Breslau laid the foundation for the 
first physiological laboratory. See 
Du Bois-Reymond, 'Reden,' vol. ii. 
p. 367. 


training-school for the greater part of the eminent 
chemists outside of Paris, and the model for similar 
establishments, and extended its influence over the 
world — into England, Scotland, and America. It also 
did more than any other institution of that kind for the 
development of ready and accurate methods of analysis, 
such as are now used in the remotest regions. But it 
was significant for German chemistry, and for the cos- ^.^^J^-^^.^ 
mopolitan character of German science generally, that g;?^^^"^^,^- 
this brilliant development of experimental research was "^^^ science. 
stimulated from two independent centres ; that German 
chemists as little as German mathematicians attached 
themselves in a one-sided manner to the Paris school. 
In mathematical science the classical style of Gauss, 
transmitted from the ancients through Newton, com- 
bined with the analytical or modern French style of 
Jacobi and Dirichlet to give to German research its 
character of universality. In a similar manner, when 
chemistry again found a domicile in Germany and be- 
came an integral portion of the university programme, 
it had been trained in two different schools. For there 
lived at that time in Sweden the eminent authority Ber- 
zelius/ who divides with Gay-Lussac the glory of being 

^ J. Jacob Berzelius (a Swede, 
1779-1848), one of the most eminent 
and industrious of chemists, had a 
great influence on the development 
of modern chemistry by the num- 
ber as well as by the accuracy of his 
experimental determinations, by his 
invention of methods and apparatus 
for analysis, and by his extensive 
proofs of several of the most im- 
portant theories. The latter di- 
rected the labours and governed the 
opinions of many — especially Ger- 

man — investigators. It was through 
him mainly that Richter's chemi- 
cal equivalents and Dalton's atomic 
theory were extensively verified and 
applied to all parts of the science, 
to organic and mineralogical chem- 
istry. He also elaborated, in close 
connection with Davy's electrical 
discoveries, his celebrated electro- 
chemical theory, which up to the 
year 1840 was very generally ac- 
cepted by chemists ; and he assisted 
through his repeated expositions 





the master of the great German chemists of the middle 
of the century. Mitscherlich at Berlin and Wohler at 
Gottingen belonged to the school of the former, whereas 
Liebig had the good fortune to be introduced through 
Humboldt into Gay-Lussac's laboratory at Paris as the 
first pupil.^ 

and criticisms in breaking down the 
older oxygen theory of acids in fa- 
vour of Davy's more general views, 
based upon his recognition of chlo- 
rine and iodine as elementary bodies. 
His handbook of Chemistry, as well 
as his ' Jahresbericht ' (from 1820), 
probably did more than any other 
publications for the diffusion of ac- 
curate chemical information. 

^ Liebig has himself, in an auto- 
biographical memoir published post- 
humously, so fully described the 
merits of the two schools, and at 
the same time given such a vivid 
picture of the truly scientific spirit 
which animated German universi- 
ties at that time, that I am tempt- 
ed to give here some extracts. Of 
his studies in Paris he says : " What 
influenced me most in the French 
lectures was their inner truthfulness 
and the careful omission of all mere 
semblance of explanations : it was 
a complete contrast to the German 
lectures, in which, through a pre- 
ponderance of the deductive pro- 
cess, the scientific doctrine had quite 
lost its rigid coherence. ... I re- 
turned to Germany (1824), where, 
through the school of Berzelius, 
... a great reform had already 
begun in inorganic chemistry. . . , 
I always remember with pleasure 
the twenty -eight years which I 
passed at Giessen : it was, as it were, 
a higher providence which led me 
to the small university. At a large 
university, or in a larger town, my 
powers would have been broken up 
and frittered away, and the attain- 
ment of the aim which I had in 

view would have been much more 
difficult, if not impossible ; but at 
Giessen all were concentrated in 
the work, and this was a passion- 
ate enjoyment." " The necessity of 
an institute where the pupil could 
instruct himself in the chemical art, 
by which I understand familiarity 
with chemical operations of analysis 
and adroitness in the use of appar- 
atus, was then in the air, and so it 
came about that on the opening of 
my laboratory . . . pupils came 
to me from all sides. . . . The 
greatest difficulty presented itself, 
as the numbers increased, in the 
practical teaching itself. In-order 
to teach many at once, an ordered 
plan was required and a progres- 
sive way of working, which had 
to be thought out and tried. . . . 
A very short time had sufficed for 
the celebrated pupils of the Swedish 
master to give to mineral analysis 
... an admirable degree of per- 
fection. . . . Physical chemistry 
. . . had through the discoveries 
of Gay-Lussac and Humboldt, . . . 
and of Mitscherlich, . . . gained a 
solid foundation, and in the chemi- 
cal proportions the edifice appeared 
to have received its coping-stone, 
. . . No organic chemistry . . . then 
existed ; Thenard and Gay - Lus- 
sac, Berzelius, Prout, Dbbereiner, 
had indeed laid the foundation of 
organic analysis ; but even the 
great investigations of Chevreul on 
the fatty bodies received for many 
years only scant attention. Inor- 
ganic chemistry still absorbed too 
many, and indeed the best, forces. 

Twenty years after Gauss's great mathematical achieve- 
ments, two new discoveries announced to the scientific 
world that Germany had again taken a foremost position 
in chemistry. These were Mitscherlich's discovery of 
isomorphism in 1819,^ and Wohler's preparation of an 
organic compound from inorganic materials in 1828.^ 

In 1830 Liebig succeeded in finally establishing that 20. 


simple and accurate method of organic analysis known organic 

^ o ./ analysis. 

by his name. Organic chemistry, in its modern sense, 

|;it 1 

The direction I had received in 
Paris was a different one. ... I 
saw very soon that all progress in 
organic chemistry depended on its 
simplification. . . . The first years 
of my residence at Giessen were 
almost exclusively devoted to the 
improvement of organic analysis, 
and with the first successes there 
began at the small university an 
activity such as the world had not 
yet seen. ... A kindly fate had 
brought together in Giessen the 
most talented youths from all 
countries of Europe. . . . Every 
one was obliged to find his own 
way for himself. . . . We worked 
from dawn to the fall of night : 
there were no recreations and 
pleasures at Giessen. The only 
complaints were those of the at- 
tendant, who in the evenings, when 
he had to clean, could not get the 
workers to leave the laboratory." 
See * Deutsche Rundschau,' vol. 
Ixvi. pp. 30-39. 

1 Eilhard Mitscherlich (1794- 
1863), a pupil of Berzelius, dis- 
covered in 1819 that in compound 
bodies which crystallise in definite 
forms certain elements can be re- 
placed by others in the proportion 
of their chemical equivalence with- 
out changing the form of crystallisa- 
tion. Such elements are termed 
*' isomorphous." Berzelius declared 

this to be the most important dis- 
covery that had been made since 
the theory of chemical proportions 
had been established. 

-' This synthesis was the prepara- 
tion of urea, a highly organic sub- 
stance, out of the compounds of 
cyanogen, with the examination of 
which he and Liebig were then oc- 
cupied. " It was the first example 
of the fact that an organic sub- 
stance could, by chemical methods 
alone, be produced out of inor- 
ganic materials ; this discovery de- 
stroyed the difference which was 
then considered to exist between 
organic and inorganic bodies — viz., 
that the former could only be 
formed under the influence of vege- 
table or animal vital forces, where- 
as the latter could be artificially 
produced" (Kopp, * Geschichte der 
Chemie,' vol. i. p. 442). It must 
here be remarked that this state- 
ment is only correct if the sub- 
stances, cyanic acid and ammonia, 
out of which Wohler produced urea, 
are considered to be inorganic ; in- 
asmuch as neither of them had then 
been produced otherwise than out 
of organic substances, the popular 
notion on W^ohler's important dis- 
covery requires this correction. See 
Kopp, * Gesch. der Wissenschaf ten 
in Deutschland,' vol. x. p. 546. 

j^ r- 



may be said to date from these and other simultaneous 
labours of Liebig and Wohler.^ But although the pure 
sciences, mathematics, physics, and chemistry, advanced 
on new lines in the hands of German students, and 
although theoretical investigations have always been 
favourite pursuits of theirs, as we shall have ample 
opportunity to note in the course of our further survey, 
the greatest contribution to the progress of science, and 
the most brilliant performances of the exact spirit of 
research which emanated from Germany during the first 
half of this century, lay in a different direction. And it 
is hard to believe that the conditions favourable to this 
peculiar growth could have been found anywhere else 
than in the German universities. The many elements of 
thought which meet on that ground, the equal dignity 

1 The joint labours of Liebig 
(1803-73) and Wohler (1800-82), 
which have become of such im- 
portance to science, form one of 
the most interesting instances of 
scientific co-operation between two 
men pursuing different lines of 
thought and trained in different 
schools. See the preface to Hof- 
mann's edition of Liebig and Woh- 
ler s Correspondence. In Liebig' s 
autobiographical sketch, quoted 
above, he thus enlarges on his re- 
lations to Wohler: "It was my 
good fortune that, from the be- 
ginning of ray career at Giessen, 
similar inclinations and endeavours 
secured me a friend, with whom, 
after so many years, I am still (be- 
tween 1860 and 1870) connected 
by ties of the warmest affection. 
Whereas in me the tendency pre- 
dominated to look for the likenesses 
of substances and their combina- 
tions, he possessed an incomparable 
talent for seeing their differences ; 

acuteness of observation was jomed 
in him to an artistic aptitude and 
to a genius for finding new ways 
and means of analysis such as few 
men possess. The perfection of 
our joint researches into uric acid 
and the oil of bitter almonds has 
been frequently praised ; this is his 
work. I cannot sufficiently estimate 
the advantage which both my own 
and our joint aims derived from my 
union with Wohler; for in them 
were combined the peculiarities of 
two schools, and the good which 
each had, attained its value through 
co-operation. Without grudge or 
jealousy we pursued our way hand 
in hand ; if one required help, the 
other was ready. An idea can be 
formed of this mutual relation 
when I mention that many of the 
smaller productions which bear our 
names belong to one alone ; they 
were charming little presents which 
one gave the other" (p. 39). 


which there belongs to pure and to applied science, 
the continual contest which exists there between meta- 
physical and exact reasoning, and the general ebb and 
flow of rival currents of ideas, all seem to have been 
necessary to raise to the rank of an exact science those 
researches which deal with the phenomena of life and 
consciousness in their normal and abnormal forms of ex- 
istence. In the hands of German students ^ chemistry 
and physics, botany and zoology, comparative anatomy oemS 
and morphology, pathology, psychology, and metaphysics, 
have laboured from different and unconnected beginnings 
to produce that central science which attacks the great 
problem of organic life, of individuation, and which studies 
the immediate conditions of consciousness. Physiology^ 
or to use its more comprehensive name, Biology^ may be 

Biology a 

^ The two greatest discoveries 
in physiology belong to England. 
These are Harvey's discovery of the 
circulation of the blood in the seven- 
teenth century, and Charles Bell's 
discovery of the difference of sensory 
and motor nerves in the early part 
of this century. The two men, how- 
ever, who have done most to estab- 
lish physiology as an independent 
science, whose systematic works 
have done most for the student 
of physiology, are probably Haller 
(see supra, p. 176), whose 'Ele- 
menta' cast into the shade all 
older handbooks, and Johannes 
Miiller (1801-.58), whose ' Hand- 
buch' (1833-40) was translated 
into French and English. See Du 
Bois-Reymond, ' Reden,' &c., vol. 
ii. pp. 143, &c., 195, 360, who also 
points out how in other sciences, 
like mathematics, physics, chem- 
istry, Germans made use almost 
exclusively of translations of French 
and English text-books and hand- 
books, whereas in physiology they 

VOL. I. 

furnished for a long period the 
systematic treatises for the whole 
world (vol. ii. p. 196). Physiology 
has therefore with some right been, 
termed a German science (see 
Helmholtz, *Vortrage,' &c., vol. i 
pp. 339, 362 ; Du Bois-Reymond^ 
'Reden,' vol. ii. p. 265). Com-*^ 
pare also what Huxley says, 
' Critiques and Addresses,' pp. 221,, 
303. On the connection of phy- 
siology with all other sciences see 
likewise Helmholtz, loc. cit. ; Du. 
Bois - Reymond, vol. ii. p. 341 ;. 
Huxley, 'Lay Sermons,' &c., p. 
75; 'Science and Culture,' p. 52:. 
"A thorough study of human phy-^ 
siology is, in itself, an educationi 
broader and more comprehensive 
than much that passes under that 
name. There is no side of the in- 
tellect which it does not call into 
play, no region of human know- 
ledge into which either its roots or 
its branches do not extend," &c. 

2 The word "biology" seems to 
have been first used by G. R^ 






theory of 

said to be a German science as chemistry has been 
named a French science. I have already referred to the 
great Haller in the last century, who may be called the 
father of physiology ; to Blumenbach, the comparative 
anatomist ; and to Liebig and Wohler, who first among 
chemists succeeded in producing an organic compound by 
the processes of inorganic chemistry. I have now to add 
two names, which together mark a great revolution in our 
ideas of the structure of organisms, and link together 
the two sciences which had treated separately of the 
animal and vegetable worlds. About the year 1838 
Mathias Schleiden ^ propounded his cellular theory con- 

Treviranus (1776-1837), a learued 
physician of Bremen, who began to 
write his ^Biologie oder Philosophic 
der lebenden Natur' in 1796 and 
to publish it in 1802 (6 vols., 1802- 
22). Lamarck used the word in 
his ' Hydrogeologie,' 1801. They, 
as well as Bichat about the same 
time, independently " conceived the 
notion of uniting the sciences which 
deal with living matter into one 
whole, and of dealing with them 
as one discipline" (Huxley, on the 
study of Biology, 1876, in 'Ameri- 
can Addresses,' p. 136, &c.) The 
term, though of German origm, has 
not found favour in that country, 
and after having been used officially 
in France and England, makes its 
appearance in Germany only since 
the great works of the modern 
English school, headed by Darwin, 
have gained so much influence in 
Germany. In the meantime the 
biological sciences had been exten- 
sively represented at the German 
universities by chairs of physiology, 
zoology, botany, &c. According to 
Huxley, biology has been "substi- 
tuted 'for the old confusing name 
of natural history," and "denotes 
the whole of the sciences which 

deal with living things, whether 
they be animals or whether they 
be plants" {loc. cit., p. 138). It 
can be divided into three branches 
— (1) Morphology, which comprises 
the sciences of anatomy, develop- 
ment, and classification ; (2) the 
science of the distribution of living 
beings, present and past ; and (3) 
physiology, which deals with the 
functions and actions of living 
beings, and tries to ''deduce the 
facts of morphology and of distribu- 
tion from the laws of the molecular 
forces of matter" (Huxley, 'Lay 
Sermons,' &c., p. 83, 1864). To 
these three Huxley adds ('Ency. 
Brit.,' art. "Biology") the infant 
science of "aetiology," which "has 
for its object the ascertainment of 
the causes of the facts of biology 
and the explanation of biological 
phenomena, by showing that they 
constitute particular cases of general 
physical laws" (p. 688). 

^ Mathias Jacob Schleiden (1804- 
81), for some time Professor of 
Botany at Jena, was a man of 
peculiar ability and disposition, 
combining a philosophical mind 
with exact knowledge and a gen- 
eral literary taste, not frequently 

same time Theodor Schwann > extended this theory to '"'"'""'• 

tTmalT""- "" ""^'^ '' circumstances combLd 
to make the announcement of the cellular theory, which 
wm always be associated with those two names, an epoch 
in the history of scientiiic. indeed of general, thought ^ 
The historian of botany, Julius Sax^hs, describes the 
pub ication of Schleiden s great work as a buJto d J 
W and Du Bois-Eeymond says : " In order to meas 1 
the niagical progress which it marks, one must have wit- 
nessed he rise of the cellular theory, when it sudden^l 
spread daylight in the darkness of the hidden struct^ I 


to be found among men of pure 
Bcience m Germany. Opposed to 
the idealistic philosophy as a fol- 
lower of Fries, and on the other side 
to the dry systematisation of the 
l^mnaean school, he was the man at 
once to broaden the scientific view 
and to create a popular interest in 
the life of the plant "-world. The 
titles of his two best known works 
are characteristic, 'Die Botanik als 
inductive Wissenschaf t ' (1842-45) 
and his short-lived periodical (filled 
with the labours of his equally im- 
portant co-editor, Nageli), ' Zeit- 
schrift fiir wissenschaftliche Bo- 

o ui'^-^i^^"^*^ *^® friendship of I 
bchleiden and Schwann (1810-82 
a pupil of Johannes Miiller and 
professor at Louvain), two inde- 
pendent courses of research and ' 
scientific thought were brought to- I 
gether. Schleiden placed the "cell" 
--a term used before him by Hooke, 
Malpighi, Grew, Wolff, Brown, and 
Mirbel— in the forefront of his de- 
scription as the element of form 
and as the origin of life, or— as we 
now express it— as the morphologi- 
cal and embryological unit, in the 
plant. A similar series of great 

names, beginning with Bichat and 
leading up to Johannes Miiller 
marks the studies of animal tissues 
Schwann struck with the analogy 
of Schleiden's nucleated cells and 
similar structures which he h^ 
! t-^'r^}'' ^^^ notochord, co^ 


tneidea that a common principle 
o deve opment exists for the mo t 
different elemental parts of the 
organism and that the format^n 
of cells is this principle." This^s 
the beginning of Ue cellular theory 

! ^h^^^. produced at once a recon-' 
struction of the whole of " general 

i anatomy" by Jacob HenleTS 
»&;, and subsequently the "celln 

As the latter has himself said, he 
aims at the establishment of a gen^ 
eral hiological principle, and thus 

Schwann is characterised as the 
transition from the " historical "to 

dpr ^if f '^"m'"' ^^^^'' 'Geschichte 

?8fi0? ono'^^^ ^^ J^^h. bis 
I860, p. 203, and in many other 
passages. ^ "I'ucr 




of animals and plants, where the rays of comparative ana- 
tomy and embryology could not reach."' This bold gener- 
alisation, which had been prepared by a long series of 
botanical and morphological researches in and out of Ger- 
many, met alternately with applause and criticism ; it gave 
rise to a long controversy, and was the starting-point of a 
whole line of important discoveries.^ It secured for Ger- 
many a long period of supremacy in physiological science. 
This supremacy was more than maintained by a great 
», volume of minute investigations, which emanated from 
^'w^&T the schools, and centred in the names, of E. H. Weber* 

seductive in an opposite direction, 
they preserved pure and undefiled 
within themselves the German ideal 
of Wissenschaft as a pursuit carried 
on for its own intrinsic value, not 
for any immediate practical object. 
Their position, especially that of 
the two elder brothers, is in this 
respect unique, and may be studied 
independently of the scientific ideas 
which they represented, and which 
will occupy us later on as a chapter 
in the history of thought character- 
istic of the German mind and the 
best type of the university studies. 
In three works of classical value — 
'Die Wellenlehre auf Experimen- 
ten begriindet' (E. H. and W. 
Weber), 1825; 'Die Mechanik der 
menschlichen Gehwerkzeuge ' (W. 
and E. Weber), 1836; ' Elektro- 
dyuamische Maasbestimmungen 
(W. Weber), 1846 onward—and in 
a great number of special investi- 
gations, the method of exact mea- 
surement was applied to physical, 
physiological, and even mental 
phenomena, and the foundation 
laid for a mechanical description 
and mathematical calculation. The 
later generalisations, known as Wil- 
helm Weber's law of electro-dyn- 
amics and E. H. Weber's law of 
psycho-physics, have given nse to 

1 Du Bois-Reymond, *Reden,' vol. 

ii. p. 541, &c. 

2 "Whatever cavillers may say, 
it is certain that histology before 
1838, and histology since then, are 
two different sciences— in scope, m 
purpose, and in dignity— and the 
eminent men to whom we allude 
may safely answer all detraction by 
a proud Circtimajaicc. "—Huxley in 
his valuable paper on "The Cell 
Theory" in the ' British and Foreign 
Medical Chirurgical Review,' 1853, 
vol. xii. p. 290. 

3 The three brothers W eber ( bmst 
Heinrich, 1795-1878; Wilhelm, 
1804-91 ; and Eduard, 1806-71) may 
be looked upon as early representa- 
tives of the best form of German 
research on the lines now recognised 
as the true and fruitful ones in na- 
tural science. Bom in an age when 
other great and more widely known 
reformers— such as Liebig, Schon- 
lein, and Joh. Miiller— freed them- 
selves with difficulty from the pre- 
vailing metaphysical systems, they 
seem to have at once seized the 
true spirit of exact research with- 
out relinquishing the broader philo- 
sophical and encyclopaedic view of 
the sciences which they cultivated. 
Living far into an age when the 
utilitarian spirit became equally 



and Johannes Miiller. The school of the latter especially and Johan- 

nes Miiller. 

has the merit of having introduced over the whole field 
of physiological phenomena exact methods of inquiry, 
of having established physiological laboratories all over 
Germany similar to Liebig's chemical laboratory at 
Giessen, and of having effectually chased away the vague 
notions of the older metaphysical school, and diffused the 
true scientific spirit. It boasts of having filled the chairs 
of medicine, physiology, and anatomy at the German 
universities with a long list of eminent teachers who have 
spread this true scientific spirit in every branch of the 
medical sciences/ which it has in consequence drawn into 

long controversies and fruitful 
theories. Their joint labours 
cover fully half a century. See 
for a sympathetic picture of the 
position which the three brothers 
Weber held in the learned world 
the biography of Fechner by Kuntze, 
1892, p. 243 : " They were among 
the first to raise the study of Nature 
among Germans to the eminence 
occupied by the philosophers and 
discoveries of the Latin races." 

^ The medical sciences, represent- 
ed by the medical faculty, but also- 
by those biological sciences which, 
like botany, zoology, anthropology, 
&c., belong to the philosophical 
faculty, now furnish the largest 
number of students to the German 
universities. In the beginning of 
the century the theological faculty, 
which then included the greater 
part of those who prepared them- 
selves for higher teaching, stood 
at the head as regards numbers. 
Under the influence of the philo- 
logico- historical movement, which 
grew and culminated in the course 
of this century, and the rising tide 
of the exact sciences, the philoso- 
phical faculty for a time gained 

and maintained the upper hand. 
Biological — including medical — 
studies now command the greatest 
attention. In his statistical report 
(contained in Lexis, ' Die deutschen 
Universitiiten,* Beriin, 1893) Prof. 
Conrad gives an interesting table 
of the changing numerical pro- 
portion in the different faculties 
(vol. i. p. 125, &c.) Prof. Billroth 
in his admirable treatise, * Ueber 
das Lehren und Lernen der medi- 
cinischen Wissenschaften,' Vienna, 
1876, deals with this subject at all 
the German universities, including 
the Austrian. As Vienna is such 
an important centre of medical 
studies, the proportion of those 
students who cultivate biological 
studies would probably be still 
greater if we were to include the 
Austrian universities. I suppose 
the figure would be about 40 per 
cent of the whole. To Billroth's 
treatise I may also refer as con- 
firming in relation to these more 
modern branches what I said above 
of the culture of Wissenschaft. See 
p. 279 and the whole section on the 
relation of the biological sciences to 
the university, pp. 411-446. It is 

It : 







the circle of the exact or mechanical sciences. But not 
only in its far-reaching applications to medical know- 
ledge and practice has the movement which centred in 
Weber and Muller shown its strength and importance ; it 
has also, from the commencement, extended its influence 
in another direction. To it belongs pre-eminently the 
cultivation of that borderland which connects the natural 
and the mental sciences. Muller ^ himself began his 
career by a study of the mechanism of the perceptions 
of the senses. He affirmed the law of srpecijic energies. 

interesting to note that Prof. Bill- 
roth does not employ the word 
biological, but uses the untranslat- 
able compound naturwissenschaft- 

1 Johannes Miiller (1801-58) has 
been termed the Haller of the 
nineteenth century, the Cuvier of 
Germany. A very good account 
of bis work, which forms an im- 
portant chapter in the history of 
German biology, is contained in Du 
Bois-Reymond's ' Gediiehtnissrede 
auf Joh. Miiller' (1858), reprinted 
with extensive notes in his ' Reden,' 
vol. ii. pp. 143-334. Miiller is there 
considered as the last representa- 
tive of a dynasty of philosophers 
who embraced the whole domain of 
"biology," which since has become 
divided into various sciences, not- 
ably the morphological and the 
physiological branches. He thus 
stands out as the master of some 
of the greatest modern represent- 
atives of natural and medical sci- 
ence, such as Schwann and Henle 
in anatomy, Briicke, Du Bois-Rey- 
mond, and Helmholtz in physiology, 
Virchow in pathological anatomy. 
He together with Lucas Schonlein 
(1793-1864) may be considered as 
the founder of the modern Berlin 
school of medicine, contemporane- 
ous with which is the modem 

Austrian school, with the names of 
Purkinje, Skoda, Oppolzer, and 
Rokitansky. An excellent charac- 
terisation of the different positions 
and influences, of the cross-currents 
of thought, of the original homes 
and of the wanderings of the scien- 
tific spirit through the many Ger- 
man - speaking countries and the 
extensive network of German uni- 
versities, will be found in Billroth, 
loc. cit. , pp. 307-366. If we imagine 
a similar life as existing all through 
the century in other domains of 
thought— in philosophy, theologj^ 
philology, mathematics, chemistry, 
law, and the science of history — we 
get a faint idea of the work of the 
German universities. In Lexis, 
'Die deutschen Universitiiten,' an 
attempt has been made to give 
such a picture. The picture, how- 
ever, suffers by the exclusion of the 
Austrian universities, and these — 
notably in the medical world — hold 
such a very high position that the 
record of the united work is some- 
what incomplete. The sciences are 
also in this record cut up into 
many branches, whereas in the 
earlier part of the century many of 
these were united and represented 
by one great name. Such a name 
was Johannes Muller in biology. 



which declares that the differences of the sensations of 
light and colour, of sound, of touch, &c., do not depend 
upon the mode of irritation, nor even upon the different 
structure of the specific nerves, but upon the nature of 
the central sense organ. In the school of Muller the 
phenomena of voltaic electricity, which had been so seduc- 
tive and misleading to an earlier school of physiologists 
not experienced in the methods of exact research, were 
again subjected to scientific investigation, and led to 
the brilliant researches with which the name of Du Bois- 
Eeymond is so intimately connected. He is as ready as 
Helmholtz, who in his two great works on physiological 
optics and musical acoustics has founded new branches 
of science,^ to acknowledge the leadership of Johannes 

1 Helmholtz (1821-95), equally 
celebrated as physiologist and ma- 
thematical philosopher, was edu- 
cated under the influence of Jo- 
hannes Miiller on the one side, of 
Jacobi and the Konigsberg school 
of mathematicians (Bessel and Neu- 
mann) on the other. If we add to 
this that he also made a profound 
study of those far-reaching specula- 
tions which originated in the phil- 
osophy of Kant, we realise how rare 
is the combination of ability and 
knowledge which he has brought to 
bear on the discussion of the most 
advanced problems in physics, 
biology, and psychology. In the 
sequel I shall have to refer so 
frequently to his writings that I 
confine myself here to giving the 
date of his principal, his epoch-mak- 
ing publications : 1847. 'Ueberdie 
Erhaltungder Kraft'; 1858. 'Ueber 
die Integrale der hydrodynamischen 
Gleichungen, welche der Wirbel- 
bewegung entsprechen ' — both re- 
printed in ' Wissenschaf tliche Ab- 
handlungen,' Leipzig, 1882 and 

1883, 2 vols. These two Memoirs 
may be considered as corner-stones 
of two of the most important mo- 
dern theories in physical science, 
the " conservation of energy " and 
the *' theory of vortex motion." In 
both, the name of Helmholtz is in- 
timately allied with that of William 
Thomson (Lord Kelvin). Equally 
important and more comprehensive 
have been his researches in the 
physiology and psychology of sense- 
perceptions in his * Physiologische 
Optik,' Leipzig, 1867; 'Lehre von 
den Tonempfindungen,' Braunsch- 
weig, 1863. 

Helmholtz has also contributed 
largely to the discussion of two very 
important branches of modern spe- 
culation — first, the theoretical views 
on the nature of electrical pheno- 
mena expressed by the opposite 
conceptions of Wilhelm Weber in 
Germany and Faraday in England ; 
second, the origin of geometrical 
axioms, especially the axiom refer- 
ring to parallel lines. A great 
interest in this subject had been 





MtiUer. And out of the circle of which E. H. Weber 
was the centre, has emanated that work of Fechner, 
* Elements of Psycho-physics,' which marks an epoch 
in psychology : it is indeed mainly occupied with the ex- 
position and application of what is termed Weber's law 
of sensation.^ In the course of the second quarter of the 
century, the names of Gauss and Jacobi in mathematics, 
of Liebig and Wohler in chemistry, of Schleiden and 
Schwann in the science of life, of MuUer and Weber in 
physiology, raised German science to the level previ- 
ously reached by the French Academicians, by Laplace 
and Lagrange, by Lavoisier and Berthollet, by Cuvier 
and St-Hilaire, by Vicq-d'Azyr and Bichat. During 

created by the posthumous publi- 
cation of Riemann's celebrated Me- 
moir, 'Ueber die Hypothesen welche 
der Geometric zu Grunde liegen,' 
Gottingen, 1865. Helmholtz's in- 
vention of the ophthalmoscope in 
1851 marks an epoch in ophthal- 

1 Gustav Theodor Fechner (1806- 
87), professor at the University of 
Leipsic, was an extraordinary man. 
The wide range of his interests and 
his great personal influence are well 
described in his biography by Dr 
Kuntze, ' G. T. Fechner, Ein 
deutsches Gelehrtenleben,' Leipzig, 
1892. Together with Lotze he may 
be said to have brought about the 
reform of German speculative phil- 
osophy, and in relation to this he 
will occupy our attention largely 
in a later portion of this book. He 
belonged to the circle of which E. 
H. Weber was the centre, and has 
taken an important place in the 
history of philosophy and science 
by his now celebrated work, ' Ele- 
mente der Psychophysik,' 2 vols., 
Leipzig, 1860 ; 2nd ed., 1890. The 

object of this work is to establish 
** an exact doctrine of the relations 
of body and mind," the principal 
task being "to fix the measure of 
psychical quantities." He says in 
the preface : " The empirical law 
which forms the principal founda- 
tion, was laid down long ago 
by different students in different 
branches, and was expressed with 
comparative generality mainly by 
E. H. Weber, whom I would 
call the father of psycho-physics" 
(Preface, p. v). In early life 
Fechner did much, by his transla- 
tions of Biot's ' Physics ' and Th^- 
nard's * Chemistry,' as well as by his 
own experimental works, to intro- 
duce the French scientific spirit into 
German research. His psycho-phy- 
sical labours have been continued 
by Prof. Wundt ; his importance 
as marking a turning - point in 
German philosophy is brought out 
in Paulsen's ' Einleitung in die 
Philosophic,' Berlin, 1890. See 
especially Preface, p. viii, and p. 
318, where Fechner is placed before 

the second half of the century, the influence of French 
thought on German science has been less marked, partly 
owing to the independent course which the latter, since 
the age of Johannes Miiller, has struck out for herself 
in the biological sciences, partly through the more inti- 
mate intercourse which has set in between English and 
German thought. The three great scientific ideas which 
the second half of the century has been establishing — the 
law of the conservation of energy, Darwin's theory of 
descent, and Faraday's novel conception of electrical 
phenomena — have been elaborated mainly by the co- 
operation of English and German research, though it 
must be admitted that at least one of these developments 
dates back to the beginnings laid by French science,^ 
whilst the views of Faraday are subversive of some of 
the fundamental notions to which the works of the great 
French mathematicians had given very general currency. 
Before we can enter more fully on a review of these more 
modern ideas, I must, however, give a picture of -the state 
of scientific thought in England during the first half of 
the century. This will be our subject in the last portion 
of the present section. 

^ Darwin's theory of descent has 
its forerunners in Lamarck and St- 
Hilaire, whose merits in this re- 
spect are supposed to have been 
overlooked owing to the overwhelm- 
ing authority of Cuvier. See Hux- 
ley, "Origin of Species" in * Lay 
Sermons,M891, p. 252; "Evolu- 
tion in Biology" in 'Science and 
Culture,' 1888, pp. 296, 313. But 
whilst it is true that Lamarck and 
St-Hilaire entertained doubts as to 
the fixity of species, the explana- 
tion of the particular manner in 
which the change of species takes 

place is entirely due to Darwin, 
and without this further step 
speculations as to the origin of 
species would have remained for a 
long time in the vague. Lamarck's 
speculations were of no real use to 
Darwin, and had besides been anti- 
cipated by Erasmus Darwin. On 
the other hand, the researches of 
Sadi Carnot were of great value in 
the hands of Joule, Thomson, and 
Helmholtz, who may be regarded 
as the founders of the doctrine of 
the conservation of energy. 






^ 25. But it is my object at present not so much to dwell 

Spmt of ex- « u jT 

Md'wr^n- ^P^° specific ideas or doctrines as on the growth, the 
ichaft, diffusion, and the general character of scientific thought, 
as this has been established by the separate contributions 
of the three nations in the course of the first half of our 
century. I therefore cannot leave the subject of German 
science without still more precisely noting the peculiar 
character which scientific thought has assumed under 
the influence of the German university system. As 
we saw before, when the spirit of exact research, mainly 
through the influence of the great French mathema- 
ticians and physicists, became diffused in Germany, 
and entered the pale of the German universities, it was 
met there by that peculiar ideal of learning which the 
German language terms Wissenschaft. This encounter 
did not everywhere produce a favourable reception for 
the new school ; but in the end it led, like every con- 
troversy, to a firmer establishment of the true princi- 
ples of research. The life of the German universities 
had in the earlier centuries begun with classical studies ; 
it had been reformed under the influence of the theo- 
logical and juridical requirements of the Protestant 
Governments; and ultimately it had been entirely re- 
newed under the influence of the classical and philo- 
sophical studies centred in the fourth or philosophical 
faculty. These classical and philosophical studies com- 
bined to create the ideal of Wissenschaft, or science, in 
the broadest sense of the word. This ideal formed the 
central conception in the new scheme of a higher and 
general education of the nation ; it accompanied the 
great revival in art, poetry, and literature. In the 


philosophy of Kant and Fichte, the republican notions 
which led the political movements in America and 
France had been reduced to a system and theoretically 
proved; the discipline of a classical education was the 
school in w^hich leaders and youths were trained who 
marched into the war against the great oppressor. This 
ideal of Wissenschaft had thus acquired a practical mean- 
ing, an ethical — not to say a religious — significance ; it 
was allied to the religious revival preached by Schleier- 
macher and a section of the Eomantic school. Of its 
value as a principle for guiding research and learn- 
ing it had given proof in that great circle of studies 
which, since the time of F. A. Wolf and Wilhelm von 
Humboldt, was comprised under the name of Philology. 
Under its influence new universities were being founded 
and academies remodelled. 

Now, it is the peculiarity of all philosophical and 
historical studies that they deal with one great subject, 
which cannot easily be divided into a number of inde- 
pendent parts capable of separate treatment ; since their 
interest attaches mainly to the fact that they explore 
the workings and manifestations of the human mind in 
the past and in the present. These studies are there- • 
fore forced to keep always in the foreground the idea 
of a great unity of action and purpose, to aim at com- 
pleteness of view, and to refer all special researches to 
general principles and standards. The encyclopaedic view, 26. 
in fact, is forced upon all philosophical and historical pi'dfcview 

. . necessary in 

sciences. Almost without exception the great masters philosophy 

*• *-' and history. 

and teachers who lived in the beginning of this century 
adhered to this view, -and however great in special and 




of Nature. 

detailed research, measured the importance of their 
results according to the light which they were able to 
throw upon the questions referring to the whole subject 
and its combined life and unity. 

It was also natural, seeing that this comprehensive 
or philosophical treatment led to such great results in 
the historical sciences, that an attempt should have been 
made to deal with the phenomena of Nature by a similar 
conception. It was not a new or a far-fetched sugges- 
tion to regard Nature as the playground of a hidden 
intelligence, of an unconscious mind, just as history, lan- 
guage, and thought were viewed as the manifestations 
of the conscious human mind. After this the further 
conception was not remote that both the mind of Nature 
and the mind of Man are only two different sides of the 
universal or absolute Mind. The philosophy of Schelling 
was the first attempt to put this idea into an applicable 
form, the system of Hegel the first confident elaboration 
of it in its various ramifications and applications. At 
the time when the mathematical and physical sciences 
were leading the way in France, and gradually forcing 
their way into Germany, most of the universities in the 
latter country had one or more representatives of that 
new and apparently promising school which termed itself 
the "Philosophy of Nature." The trammels of this school 
had to be shaken off by those who, as they became 
gradually convinced of its barrenness in actual results, 
took up the cause of the exact or mathematical sciences 
now that they had been cultivated by many isolated 
labourers in Germany and in England, and had been 

for the first time connected into a great organisation by 
the French Academy of Sciences. 

The opposition in which the new school of exact and 28. 
detailed research stood to the representatives of the broad tween^the " 
philosophical view gave rise to a great many currents ^l^^^^^^ ^^ 
of thought ; for neither the former nor the latter pre- ""^^ '''^'''• 
sented a united front. Among those who advocated the 
exact methods of research there was a section which 
clung more exclusively to the empirical side, and culti- 
vated the descriptive and experimental sciences ; whereas 
others, whom we may call the French school of science, 
developed the mathematical methods, not without a cer- 
tain ill- disguised contempt for pure empiricism.^ On 
the side of classical and philosophical studies there was 
a section which cultivated the historical ^ in contradis- 

^ On the relations of mathemati- 
cal and experimental physics, and 
the diflferent opinions which existed 
during the first half of the century, 
see Helmholtz's popular addresses 
in many places, but especially the 
discourse on Gustav Magnus (1802- 
70), who may be regarded as a 
representative of the experimental 
school in Germany. In the opin- 
ion of this school, which cultivated 
the borderland of physics and chem- 
istry, of organic and inorganic phe- 
nomena, or investigated the less 
known phenomena of frictional elec- 
tricity (Riess) or the complicated 
phenomena of meteorology (Dove), 
a danger existed that mathematical 
theories and elaborate calculations 
might lead to an estrangement from 
nature and observation, similar to 
that which speculative philosophy 
had created before. Helmholtz him- 
self was met by this sentiment when 
he published his great memoir, 

'Ueber die Erhaltung der Kraft,' 
in 1847 ; Poggendorf's physical 
periodical would not receive it, 
and Jacobi, the mathematician, 
was the only one who showed any 
interest in it. See Helmholtz, 
* Wissenschaftliche Abhandlungen,' 
vol. i. p. 73; 'Reden,' vol. ii. p. 

2 As the philosophy of ScheUing 
promoted a study of nature, and in 
doing so prepared its own downfall, 
so the philosophy of Hegel led to a 
study of history, and thus to the 
proof of the insufficiency of its own 
generalisations. Many valuable be- 
ginnings of historical research eman- 
ated also from the Romantic school 
of literature. In all these instances 
philosophical interests led beyond 
the abstract logical and metaphysical 
treatment into the broad and fertile 
plains of actual life, be it that of 
nature or of art or of history. But 
the true methods of research in 






von Hum- 

tinction to the philosophical view, and another which 
elaborated what it termed exclusively the critical meth- 
ods/ not without a certain suspicion regarding those who 
showed a desire to roam into outlying fields which did 
not permit of equally strict discipline and treatment. So 
far as this refers to the purely historical sciences, I 
shall revert to the subject when I come to treat of the 
principles which underlie and guide this line of studies. 
At present I am concerned with the growth and dif- 
fusion of the exact scientific spirit and its methods. 

No one did more to spread the ideas and methods of 
French science in Germany than Alexander von Hum- 
boldt. He himself had done original scientific work" be- 

these extensive fields were after- 
wards found not so much in philo- 
sophical canons as in a love of detail 
and observation, and in the exercise 
of an unbiassed criticism of facts 
and records. For the relations of 
philosophy to history in respect of 
this, see Wegele, ' Geschichte der 
deutschen Historiograph ie,' Miin- 
chen, 1885, 5th book, p. 975, &c. 
Equally important are — Gervinus, 
' Grundziige der Historik,' Leipzig, 
1837 ; the ' Nekrolog auf Schlosser,' 
Leipzig, 1862, including the whole 
literature which it provoked ; and 
O. Lorenz, 'Die Geschichtswissen- 
schaft,' Berlin, 1886, especially the 
first chapter. 

^ On the Critical school of phil- 
ology, and the wider and narrower 
sense in which the aims and meth- 
ods of the science of antiquity were 
defined, see Bursiau, ' Geschichte der 
classischen Philologie in Deutsch- 
land,' Miinchen und Leipzig, 1883, 
p. 665, &c. ; also O. Ribbeck, ' Fried- 
rich Ritschl,' Leipzig, 1879 and 
1880. Further, the essays on Bockh, 
K. 0. Miiller, and Georg Curtius in 
the third volume of Ernst Curtius, 

' Alterthum und Gegenwart,' Berlin, 
1889 ; and, finally, the chapter on 
"Klassische Philologie" by Wila- 
mowitz-MoUendorf in Lexis, * Die 
deutschen Universitaten, ' vol. i. p. 
457, &c. 

^ Alexander von Humboldt (1769- 
1859) published in 179 7, shortly after 
Galvani's great discovery, his ' Ver- 
suche liber die gereizte Muskel- und 
Nervenfaser.' In the history of sci- 
ence his name will live as that of 
the man who organised that " scien- 
tific conspiracy of nations " which is 
peculiar to our century, and with- 
out which the study of geography, 
meteorology, astronomy, the phe- 
nomena of tides and magnetic dis- 
turbances — called by him magnetic 
storms — could not effectually be 
carried on. The fact also that on 
his return from his great travels he 
became next to Napoleon Bona- 
parte the most famous man in 
Europe, did more than anything 
else to raise the natural sciences in 
the popular mind to thatf eminence 
which earlier belonged to polite 





fore he left Germany for the extensive travels by which 
he became celebrated, and through which he founded a 
new science — the science that deals with the geographical 
distribution of plant life. Moreover, his absence from his 
native country fell within that period during which the 
philosophical school, headed by Schelling and Hegel, at- 
tained to its greatest power. He was never drawn into its 
vortex; on the contrary, he maintained a lifelong protest 
against the spirit of its doctrine at a time when the circle 
which surrounded him at Berlin came under its powerful 
influence.^ He led a long line of ardent young workers 
both to the right sources of scientific knowledge and 
to an ultimate victory over the opposed school of 
thought. Though not a profound mathematician him- 
self, he appreciated the part which mathematics were 
destined to play in science. Among other things, he 
protected and encouraged younger mathematical talents, 
and tried to draw Gauss from the solitary heights which 
he inhabited into the midst of the scientific circles of 
the day.^ Then there was the great influence which 

1 Cf. p. 178, note 1. It has latterly 
become the fashion to say so much 
against the mistaken methods of the 
Naturphilosophie that it is well to 
remember how many men of fore- 
most rank in the natural sciences 
belonged at one time to this school 
or were influenced by it. Foremost 
of all stands Oken (1779-1851), the 
founder of the German Association 
of Science, and editor of the peri- 
odical ' Isis.' Further, the compara- 
tive anatomist Cams (1789-1869) ; 
Oersted (1777-1851), the discoverer 
of electro-magnetism ; Kielmeyer, 
the friend of Cuvier (1765-1844) ; 
Ignaz Dollinger (1770-1841), one of 

the earliest evolutionists ; D. G. 
Kieser (1779-1862), a medical 
teacher of great influence. More 
or less influenced by the teachings 
of this school were Goethe (1749- 
1832) ; Karl Ernst von Baer (1792- 
1876), whose impartial opinion on 
the Naturphilosophie as early as 
1821 is important. Further, Lie- 
big (1803-73); Johannes Miiller 
(1801-58) ; Roschlaub (1768-1835) ; 
Schonlein (1793-1864), the founder 
of what is called the "natural- 
history" school of medicine. 

^ See A. von Humboldt's Life by 
Bruhns, translated by Lassell, 1873, 
vol. ii. p. 145 sqq. 







Influence of 
on German 

Berzelius exerted on German science through his teach- 
ing and his writings. From him emanated that great 
perfection of the purely experimental methods which 
in his own hands, as well as in those of Wohler, Mit- 
scherlich, Magnus, and others, led to an accumulation 
of detailed knowledge in chemistry of unforeseen im- 
portance and magnitude. His own annual reports, as 
well as Gmelin's celebrated handbook of chemistry, are 
monuments of this unparalleled industry. 

Others, like Liebig, Johannes Mliller, Lucas Schonlein, 
freed themselves under the influence of French science,^ 
or by their own deeper insight, from the sway of the 
false and misleading philosophy to which they had at 
one time listened. A third section started from philo- 
sophical premisses, but from premisses opposed to the 
doctrines of Schelling and Hegel. 

The school of Fries,^ in which Schleiden was the most 

^ English science had an import- 
ant but less marked influence on 
the development of naturalistic and 
medical studies in Germany. So 
far as the latter especially are con- 
cerned, see Billroth, ' Ueber das 
Lehren und Lernen der medici- 
nischen W'issenschaften an den 
Universitiiten der deutschen Na- 
tion,' Wien, 1876, p. 33. He 
roughly divides the medical schools 
of Germany into two groups, both 
descending from Boerhaave : the 
one, the modern Berlin school of 
Mliller, Schonlein, Romberg, and 
Virchow, through Haller, Reil, 
Hufeland, and Roschlaub ; the 
other, the modem Vienna school 
of Oppolzer, Rokitansky, and Bill- 
roth, through Gerhard von Swiet- 
en, De Haen, Stoll, Frank, Pur- 
kin je, and Skoda. Of French 
names which had great influence 

he gives Broussais, Corvisart, Bayle, 
Cruveilhier, and Laennec ; of Eng- 
lish, John Hunter, Matthew Bailie, 
and Astley Cooper. He gives also 
the name of Immanuel Kant as 
an important influence in the de- 
velopment of the German schools of 

2 Jacob Fries (1773-1843) pro- 
fessor at Heidelberg and Jena, led 
the critical philosophy of Kant into 
the channels of psychology and an- 
thropology. During the heyday of 
transcendental philosophy, the phil- 
osophy of Fries, like that of the 
Scotch school, was regarded with 
contempt by Hegel, and even by 
Herbart, the opponent of Hegel. It 
succeeded, however, in the end in 
influencing a considerable number 
of philosophical minds, who carried 
philosophical thought into the in- 
ductive sciences. Besides the psy- 


illustrious name, carried on within the pale of the 
philosophical school of science itself a successful opposi- 
tion to the philosophy of Nature.^ But whilst much good 
and sound work was done by many who were content 
to remain outside of the favoured studies which set the 
tone of university culture during the classical and philo- 
sophical period of German thought, the great attack 
upon the mistaken canons of the philosophy of Nature 
came from that science which had probably suffered 
more than any other under the baneful influence of 
hollow theories and empty phraseology. 
^ Helmholtz describes the despair which had taken hold 
of thinking minds in the medical profession ^ : " My edu- 
cation fell within a period of the development of medi- 
cine when among thinking and conscientious minds there 
reigned perfect despair. It was not difficult to under- 
stand that the older and mostly theorising methods of 
treating medical subjects had become absolutely useless. 
But with the theories the facts which underlay them 
were so indissolubly entangled that these 4 wo were mostly 
cast overboard. How the science must be newly built up 
the example of the other natural sciences had made clear, 
but yet the new task stood of giant-height before us. A 
beginning was hardly made, and the first beginnings were 

of Nature 
and medical 




chologist Beneke and the theologian 
De Wette, these were principally 
members of the Jena school, Apelt, 
Schlomilch, and others, who edited 
' Abhandlungen der Fries'schen 
Schule,' Jena, 1847 ; and foremost 
among them Schleiden, the reformer 
of botany in Germany. Schleiden's 
great work appeared with the title 
' Botanik als inductive Wissenschaf t. ' 
It opened with a philosophical in- 

VOL. I. 

troduction of 131 pages, in which 
inductive reasoning is recommended 
in opposition at once to the trans- 
cendental NcUurphUosophiet and to 
dry empiricism. See Sachs, *Ges- 
chichte der Botanik,' p. 203, &c. 

1 See Schleiden, ' Schelling's und 
Hegel's Verhaltniss zur Naturwis- 
senschaft,' Leipzig, 1844. 

2 See Helmholtz, 'Vortrage und 
Reden,' vol. L p. 361. 



often very crude. We cannot wonder if many honest, 
serious, thinking men then turned away in dissatisfaction 
from medicine, or if they from principle embraced an 
extreme empiricism." ^ " But the right kind of work 
brought forth its fruits much sooner than many had 
hoped. The introduction of mechanical notions into the 
theories of circulation and respiration, a better insight 
into the phenomena of heat, the more minutely elabor- 
ated physiology of the nerves, speedily produced practical 
results of the greatest importance ; the microscopical ex- 
amination of parasitic tissues, the stupendous development 
of pathological anatomy, led irresistibly from nebulous 
theories to real facts." And again ^i "Whilst in the 
investigation of inorganic nature the different nations of 
Europe progressed pretty evenly, the recent development 
of physiology and medicine belongs pre-eminently to 
Germany. The questions regarding the principle of life 

1 Cf. Helmholtz, ibid., vol. ii. 
p. 178, in his discourse **Ueber das 
Denken in der Medicin " : * * At that 
time there were many among the 
younger doctors who, in despair 
about their science, gave up all 
therapeutics, and took to empiri- 
cism, such as was then taught by 
Rademacher. This on principle 
regarded as vain all hope of scien- 
tific insight." Not only the ex- 
treme empiricism of Rademacher 
(1772-1850), but still more the wild 
theories of Hahnemann (1755-1843) 
found during this age of general 
unsettlement many followers. See 
on the origin, the principles, and 
the spread of homoeopathy, Haser, 
* Geschichte der Medicin,' vol. ii. p. 
793, &c. Haser gives the year 1816 
as the date at which Hahnemann's 
doctrines began to be accepted in 
wider circles. "It must not be 

forgotten that the heyday of ho- 
moeopathy fell in that age when 
medicine, especially in Germany, 
was in a very deficient state, so 
that the accusations raised by 
Hahnemann and his adherents did 
not appear quite unfounded. It is 
even to be admitted that homoeo- 
pathy has contributed to the re- 
action through which in our times 
the regeneration of the art of heal- 
ing has been brought about, though 
this would have taken place with- 
out Hahnemann" (p. 803). Homoeo- 
pathy has no scientific represen- 
tative at any of the German 
universities, and yet it is admitted 
that it "still enjoys a great repu- 
tation in some influential circles 
among the general public" (Hirsch, 
' Gesch. d. medicinischen Wissen- 
schaften,' p. 570). 

2 Helmholtz, loc. cit., vol. i. p. 362. 

jk k. 



are closely allied to psychological and ethical questions. 
To start with, here also that untiring industry is required 
which applies itself to pure science for purely ideal pur- 
poses, without immediate prospects of practical usefulness. 
And indeed we may glory in the fact that in this German 
scholars have always distinguished themselves by their 
enthusiastic and self -renouncing diligence, which labours 
for inner satisfaction and not for outer success." 

This habit of self-renouncing labour, of singleness of 32. 

^ -i.^i-ii,. . ,. Science for 

purpose — m snort, the ideal of pure science and its pur- its own sake, 
suit — had been elaborated in many a secluded workshop 
of a retired German university mainly under the influence 
of the classical and philosophical studies of the end of 
the last and the beginning of the present century. It was 
held up high and conspicuous by the priests of humanity, 
beginning with Lessing, Herder, and Kant, and ending in 
Schleiermacher, Hermann, and Bockh, at the head of a 
great army of devoted followers, travelling through the 
wilderness of national depression, barbarism, and despair 
into the promised land of freedom, culture, and hope. 
Such an ideal is of priceless worth, and it is this ideal 
which the philosophical and classical school of thought 
bequeathed during the first half of the century to that 
new school of thinkers which was destined to study, in 
an equally patient and unselfish spirit, the seemingly less 
elevated, but not less mysterious and fascinating, prob- 
lems of Nature. Truly Gauss, Weber, and Johannes 
Mliller worthily headed the new army of labourers. 

But though the elevated spirit in which scientific work ^ ^^3^ ^^ 
is carried on may be the most valuable bequest of the ^^^S^ 
classical and philosophical to the exact and empirical Ic&T^ 





* t 

school, there were certain more tangible characteristics 
of German research, which were carried over from the 
older to the modern type of thought. It will be useful 
to define these more clearly. 

In the course of the second half of the eighteenth 
century German literature and German philosophy had 
started from the beginnings laid by other nations, and 
after mastering and appropriating their achievements, 
had set out for a new course and a higher flight. Milton 
and Shakespeare ' in epic and dramatic poetry ; Ossian, 
the Percy Ballads, and Burns in song and lyric ; Gibbon 
in history ; Joseph Scaliger and Bentley in philology ; 
Locke, Hume, and Spinoza in philosophy ; Eousseau m 
ppose,— all these great names of a later or earlier past 
had become familiar watchwords to German poets or 
students— to Lessmg, Herder, and Goethe, to Schlegel, 
F A. Wolf, and Wilhelm von Humboldt, to Bockh, Her- 
mann, and Niebuhr, to Kant, Fichte, and Jacobi, before 
they came forward with their own creations. The same 
cosmopolitan spirit of looking elsewhere and everywhere 
for beginnings, and for co-operation in the united work 
of learning ; the same historical taste, the same desire to 
glean from all quarters,— characterised the early decades 
of the revival of German science. Hence the many 
periodicals and annual reports ; hence the fact that the 

German readers only through 
Goethe and Schlegel. Similarly 
the reaction against the school of 
Leibniz and Wolff in philosophy 
began with Kant's reply to Hume's ' 
sceptical philosophy, whereas the 
study of Spinoza influenced Kant s 
followers and opponents, Jacobi, 
Fichte, and Schelling. 

1 These names are not given as 
they follow in time, but as they 
followed in their influence on Ger- 
man thought and literature. Thus 
the early representatives of the 
German revival were influenced by 
Milton and Pope more than by the 
greater Shakespeare : epic and di- 
dactic preceded dramatic poetry : 
Shakespeare was made familiar to 


-I ^ 


nation which requires them least ^ possesses the most ^^^34.^^ 
and the best translations of foreign authors. But the S'o'ro^^h- 
quality of greatest value for science which springs from search! '^' 
the cosmopolitan and historical spirit is that of complete- 
ness and thoroughness of research. 

Secondly, the German man of science was not only 
thorough, but was as little as the German philosopher 
or classicist had been, an isolated thinker. He was 
neither the member of an academy only, nor a solitary 
genius reduced to the resources of his own study. He 
lived mostly at a university, surrounded by others, whose 
labours came in contact with his own, or who treated the 
same subject from a different point of view. He had thus 
to define the limits of his science, and to see that no part 
of the common field was left uncultivated and unexplored. 
His object could not be to produce simply a work of indi- 
vidual greatness or of finished artistic merit; his work 
was an integral portion of the one great science; his 

^ This must not be misunder- 
stood. A knowledge of the master- 
pieces of foreign literature was as 
necessary to the development of 
the German mind as it is to that 
of any other nation ; it was and 
is more complete there than in any 
other country : what I mean is, 
that as a knowledge of French and 
English has been for a long time 
so common among the educated 
classes in Germany, translations are 
more easily dispensed with there 
than in other countries. In spite 
of that, German literature abounds 
in excellent translations of the 
classics of France and England 
both in general literature and in 
science. It is also interesting to 
note that no modern language 
has succeeded so well in imitating 
foreign and classical ms^tiyoti as .the 

German, hexameters having become 
domiciled in Germany through Voss 
and Goethe, the Alcaic and Sapphic 
metres through Klopstock and Her- 
der, the more complicated stanzas 
through Platen, and above all 
through Donner's excellent ren- 
derings of the Greek dramatists. 
Riickert excelled in the imitation 
and reproduction of Persian, Indian, 
and Arabic poetry, and through him 
and Friedrich Bodenstedt German 
literature has been enriched by 
many lines of which it would be 
difficult to say whether their home 
was in Germany or in the far East, 
so perfectly is the spirit and dic- 
tion reproduced. The well-known 
' Weisheit des Brahmanen ' of 
Riickert, and Bodenstedt's 'Mirza 
Schaffy ' are examples. 

I V 



tion of re- 
search and 




labours had to fit in with the general plan, to find a 
place in the one great edifice. 

Thirdly, the German man of science was a teacher ; he 
had to communicate his ideas to younger minds, to make 
the principles and methods of research clear, to guarantee, 
in his course of lectures, something like completeness, 
to give a comprehensive survey ; not to teach " une 
science faite," but to draw out original talent in others, 
to encourage co-operation in research, to portion out the 
common work to the talents which surrounded him, or it 
might be to direct the flight of the aspiring genius.^ 

* Here the two main objects of 
academic teaching are to impart 
a knowledge of the right method 
in the special science, and to give 
a survey of the whole domain 
of the science. The two principal 
institutions by wliich these ob- 
jects are attained were first set 
going in the classical branches of 
study, and may be defined by two 
terms — the " seminary " and the 
lecture on "encyclopaedia." Both 
terms are taken from earlier insti- 
tutions. The seminary was origin- 
ally a training - school for priests 
or teachers. Under such masters 
of methodical research as F. A. 
Wolf and Gottfried Hermann, the 
institution acquired a different 
character. "The seminaries are 
the real nurseries of scientific 
research. They were founded, in- 
deed, with a different object ; the 
first seminaries, the philological 
seminaries, which were started 
during the last century at Halle 
and Gottingen, were or should have 
been pedagogic seminaries for the 
future masters in the learned 
schools. In reality they were — 
especially that of F. A. Wolf — 
in the first place institutions in 
which the art of philological re- 
search was taught. This is even 

more the case in the philological 
seminaries and societies which 
during the nineteenth century 
have been conducted by G. Her- 
mann, Fr. Thiersch, Fr. Ritschl, and 
others : they were nurseries of 
philologists, not of teachers. And 
the same may be said of the num- 
erous seminaries which in modem 
times have grown up in the other 
sciences within the philosophical 
faculty, and also in the faculties 
of theology and law : they set up 
as their aim — with few exceptions 
— the training for scientific work 
and research, not the utilisation of 
kaowledge for a practical purpose " 
(Paulsen in Lexis, 'Die deutschen 
Universitaten,' vol. i. p. 74, &c.) 
The same idea was in the mind of 
Liebig when he started the first 
chemical laboratory at Giessen (see 
supra, p. 188, note). The ency- 
clopaedic treatment of every large 
subject in a special course of lec- 
tures arranged for this purpose 
had the object of preventing the 
different studies from falling asun- 
der or ultimately failing to unite 
in the realisation of one great aim. 
This great aim of all philological 
studies, for instance, was always 
held up by men like Wolf, Her- 
mann, Bockh, and Ritschl, among 




Lastly, the German man of science was a philosopher. se. 

•^ . Combina- 

Whatever his aversion might be to special philosophical *|!?^^°^^j^^ 
doctrines, he had generally come under the influence of pJ^iiosop^y. 
some philosophical school, the teaching of which he desired 
either to uphold or to combat. Sooner or later, con- 
sciously or unconsciously, he had to make clear to him- 
self and to his disciples the underlying principles which 
he thought the right ones, to defend them against attacks 
from others, or to modify them, as progressing research 
made it necessary. If the historical sciences had bene- 
fited most by the philosophy of Schelling and Hegel, 
which attempted to give new and constructive views 
on the intellectual and ethical manifestations of the 
human or the general soul, the mathematical and phy- 

whose favourite lectures were those 
on "encyclopaedia" of philology. 
Something similar existed, and 
exists still, in theology, law, and 
what are called *' Staatsioissen- 
schaften." All these terms are 
supposed to embrace a variety of 
studies which are organically com- 
bined in one whole, forming a cycle. 
In philosophy proper Hegel, and 
later Lotze, delivered well-known 
and largely attended lectures under 
the title of Encyclopaedia. This is 
a remnant of the encyclopaedic or 
organic treatment of knowledge 
sketched out by Bacon, and pro- 
posed as a basis for their celebrated 
work by Diderot and D'Alembert 
(see ante, p. 35 and note). The 
encyclopaedia, as a learned diction- 
ary, we have seen, has since become 
merely a synopsis. How different 
from this was the truly encyclo- 
paedic treatment given by men like 
Bockh can be seen from his cor- 
respondence with K. 0. Miiller, 
where he scolds his younger friend 
for undertaking to write the article 

" Topography of Athens " for " such 
a cursed publication as an encyclo- 
paedia," whereas he himself was 
regularly lecturing on "encyclo- 
paedia of philology," in which he 
took in earnest the idea of classi- 
cal philology as "the historical 
science of the life of the ancient 
peoples" (see Curtius, 'Alterthum 
und Gegenwart,' vol. iii. p. 138, &c.) 
Now although the exact sciences 
when they became domiciled in the 
German universities did not in 
general copy this institution, yet 
the historical and philosophical 
survey, giving method and unity 
to a large circle of studies, has been 
upheld by many among the fore- 
most men of science, especially in 
the medical faculty. Of these I 
only mention Joh. Miiller (see Du 
Bois-Reymond, ' Reden,' vol. ii. pp. 
195, 279) and his pupil and follower 
Jacob Henle, who in his lectures 
on anthropology took a philosophi- 
cal survey of the whole subject of 
the medical studies^ (see 'Jacob. 
Henle' by Meckel,, p. 2X1, &c.), 


grown out 
of science 
and philo- 
sophy com- 



sical sciences have been most afiected by the spirit of 
Kant's philosophy, which has ineradicably engrained in 
the German mind the necessity of a criticism of the 
principles of knowledge. Ever and anon some of the 
most brilliant intellects in mathematics and science have 
reverted to the same problems, and, on the whole, they 
have confirmed the position taken up by Kant a cen- 
tury ago. 

It was thus under the influence of the exact methods 
of experiment and calculation taught by the great French 
school in the beginning of the century, and at the same 
time through the philosophical spirit peculiar to German 
science, that in the middle of the century the different 
sciences which deal with the phenomena of life and con- 
sciousness were remodelled. The great science of biology, 
based upon mechanical principles, was thus created, and 
the results gained in it brilliantly applied to the reorgan- 
isation of the medical profession. But this great reform 
does not belong exclusively to one great name ; it is the 
work of a long line of thinkers : nor can I conceive that 
the exclusive employment of the methods of exact re- 
search would have so effectually brought it about, unaided 
by the philosophical, historical, and critical spirit which 
formed the peculiar characteristic of German thought 
before the' exact methods had been generally introduced. 
And just because this reform required to be effected from 
so many different beginnings, and gradually elaborated 
and defended before it became firmly established, do the 
modem sciences of physiology and pathology deserve to 
be termed pre-eminently German sciences ; for no other 

* 4 



country possessed the necessary conditions and extensive 
organisations, the habits of combined study and patient 
co-operation, the large views and the high aims, which 
had been acquired at the German universities under the 
guidance of the German ideal of Wissenschaft, and under 
the sway of the philosophical and classical spirit. 

A great authority,^ who as much as any one represents 
the modern as distinguished from the earlier views in 
biological science, reviewing the different agencies which 
have brought about the great change, speaks thus. He 
is referring to Johannes Mliller, the father of modern ss. 
physiology. " The modern physiological school," he says, Reymond 

^ ^ on Mliller. 

" With Schwann at its head, has drawn the conclusions for 
which Mliller had furnished the premises. It has herein 
been essentially aided by three achievements which Mliller 
witnessed at an age when deeply-seated convictions are 
not easily abandoned, I mean, first of all, Schleiden and 
Schwann's discovery, that bodies of both animals and 
plants are composed of structures which develop inde- 
pendently, though according to a common principle. This 
conception dispelled from the region of plant-life the idea 
of a governing entelechy, as Midler conceived it, and 
pointed from afar to the possibility of an explanation of 
these processes by means of the general properties of 
matter. I refer, secondly, to the more intimate know- 
ledge of the action of nerves and muscles, which began 
with Schwann's researches, in which he showed how the 
force of the muscle changes with its contraction. In- 
vestigations which were carried on with all the resources 

* See Du Bois-Reymond, *Reden,' vol. ii. p. 219, &c. 

^iii : ! 




of modern physics regarding the phenomena of animal 
movements, gradually substituted for the miracles of 
the 'vital forces' a molecular mechanism, complicated, 
indeed, and Ukely to baffle our efforts for a long time to 
come, but intelligible, nevertheless, as a mechanism. The 
third achievement to which I refer is the revival among 
us by Helmholtz and Mayer of the doctrine of the con- 
servation of force. This cleared up the conception of 
force in general, and in particular supplied the key to a 
knowledge of the change of matter in plants and animals. 
By this an insight was gained into the truth that the 
power with which we move our own Umbs (as George 
Stephenson did those of his locomotive) is nothing more 
than sunUght transformed in the organism of the plant: 
that the highly oxygenated excrements of the animal 
organism produce this force during their combustion, and 
alon'' with it the animal warmth, the irvtviia of the 
3, ancilnts. In the daylight which through such know- 
;i'?'aban. ledge penetrated into the chemical mechanism of plants 
''°°"'' and animals, the pale spectre of a vital force could no 
more be seen. Liebig, indeed, who himself stood up so 
firmly for the chemical origin of animal heat and motive 
power, still retains an accompanying vital force. But 
this contradiction is probably to be traced to the cir- 
cumstance that the celebrated chemist came late, and as 
it were from outside, to the study of the phenomena of 
Ufe. And even Wohler still believes in a vital force, he 
who in his time did more than any one to disturb the 
vitalistic hypothesis through his artificial production of 


It was a process of critical sifting similar to that which 
Kant ^ applied to our general metaphysical ideas, which 
in the middle of the century, through the writings of 
Berzelius and Liebig, of Schwann and Schleiden, of Henle, 
Lotze, and Du Bois - Eeymond, gradually dispelled the 
older confused notions, and firmly established the mech- 40 
anical view in the study of the phenomena of life. But fit^""' 
as we are forced to recognise the substance of much of ^'°^°^* 
Kant's philosophical criticism in the lucid expositions 
of Locke and Hume before him, so it has been pointed ' 
out that the words of the eminent French physiologist, 
Vicq-d'Azyr, contain the substance of the more modern 
ideas on life.^ It required the co-operation of the exact 



^ The great influence which be- 
longs to Kant in the development 
of modern German science has been 
frequently dwelt on. In more re- 
cent times some of the first repre- 
sentatives of the medical and bio- 
logical sciences have dealt with the 
subject, and the opposition which 
fifty years ago originated in the ex- 
travagances of some of Kant's suc- 
cessors, has given way to a renewed 
recognition of the just claims of 
Kant. We may refer to Du Bois- 
Reymond, who, forgetting Lotze, 
calls Kant the last philosopher who 
took a part in the work of the 
naturalist ('Reden,' vol. i. p. 33); 
to Helmholtz, who in many passages 
of his popular addresses refers to 
the merits of Kant (' Vortrage und 
Reden,' 1884, vol. i. pp. 44, 368 ; ii. 
58, 227, 234, 248, &c.) ; to Haeser 
('Geschichte der Medizin,' vol. ii. 
p. 811). I will add to these the 
opinion of so great an authority as 
Prof. Billroth of Vienna, who, speak- 
ing of the two modern schools of 
medicine in Germany, says (* Lehren 

und Lernen der medicinischen Wis- 
senschaften,' &c., p. 334): "How- 
ever great the degree of independ- 
ence may be which the two parallel 
schools have attained, they would 
hardly have developed so rapidly 
without the powerful influence 
which came from France and in a 
lesser degree from England ; nor yet 
without that of Immanuel Kant, 
who in his ' Autophysiology of 
Reason ' enlightened German minds 
regarding their own selves, and 
who with his lively imagination fer- 
vently embraced natural science." 

^ The remarkable passage re- 
ferred to is quoted by Du Bois- 
Reymond ('Reden,' vol. ii. p. 27): 
" Quelqu' etonuantes qu'elles nous 
paraissent, ces fouctions {viz., dans 
les corps organises) ne sont-elles 
pas^ des effiets physiques plus ou 
moins composes, dont nous devons 
examiner la nature par tous les 
moyens que nous fournissent I'ob- 
servation et I'exp^rience, et non 
leur supposer des principes sur 
lesquels I'esprit se repose, et croit 



spirit of research with the critical methods acquired m 
the school of philosophy, and the exhaustive survey of 
a large array of facts acquired through historical and 
classical studies, before the significance of this brilliant 
aper^ became evident; before the underlying ideas could 
become useful guides of research and progress. " Tant^ 
molis erat Eomanam condere gentem." 

Though the reform of the biological ^ sciences, and their 
application to pathological inquiries, are probably the 
greatest achievement which the methods of exact re- 
search, in conjunction with the philosophical spirit, can 
boast of in Germany in the century, the same habit 

avoir tout fait lorsqu'il lui reste 
tout h faire." This was said at 
the end of the last century, and 
fifty years later Du Bois-Reymond 
{loc. cit.) could complain that the 
truth conteined in these words was 
not yet generally admitted, in spite 
of the labours of Berzelius, Schwann, 
Schleiden, and Lotze. Compare 
also A. von Humboldt's own con- 
fessions on this point in his ' An- 
sichten der Natur,' vol. ii. p. 309, 
&c., edition of 1849. 

1 I must remind the reader here 
that though I use the word biolo- 
gical as denoting the more recent 
point of view from which all pheno- 
mena of the living world are being 
grouped and comprehended, and 
though the word seems to have 
been first used by a German, never- 
theless the arrangement of studies 
at the German universities has 
hardly yet recognised the essen- 
tial unity of all biological sciences. 
They are unfortunately still divided 
between the philosophical and the 
medical faculties. It is indeed an 
anomaly, hardly consistent with 
the philosophical and encyclopaedic 

character of German research, that 
pakeontology, botany, zoology, and 
anthropology should belong to the 
philosophical, whereas anatomy, 
physiology, and pathology are 
placed in the medical faculty. 
Eminent biologists and anthropo- 
logists, such as Schleiden, Lotze, 
Helmholtz, and Wuudt, have ac- 
cordingly belonged to both facul- 
ties. To place biological studies 
on the right footing would re- 
quire a mind similar to that of 
F. A. Wolf, who evolved out of 
the vaguer idea of hunmniora the 
clearer notion of a "science of an- 
tiquity," and who accordingly was 
able to convert the training-school 
of teachers, the seminary, into a 
nursery of students of antiquity. 
Whether a similar reform in the 
purely scientific interests of the 
"science of life," which is now 
mostly cultivated for the benefit 
of the medical practitioner, can be 
effected in this age, when practical 
aims are gradually taking the place 
of scientific ideas, is another ques- 


of thought has shown itself in other fields of research, 
and led to similar innovations. I will here only mention 
one other line of inquiry, where neither exact nor meta- 
physical reasoning alone suffices, but where a combination 
of both is essential. I mean the gradual change which, ^^.^.4i.^ ^^ 
mainly through the writings of German mathematicians, Pf°«^p;«f 
has come over our fundamental conceptions in the region °^*^<^^- 
of geometry, algebra, and the theory of numbers. This 
subject belongs so essentially to the domain of pure 
thought that a history of thought seems specially called 
upon to take notice of it. Accordingly I intend to devote 
a special chapter to it. At present it interests us mainly 
because it is an outcome of that peculiar modification 
which the exact or scientific spirit of thought underwent 
when, introduced by French and English models, it came 
in contact with the philosophical and classical ideal of 
learning in Germany. I will repeat more clearly and 
concisely what I mean. The exact methods of thought, 
mainly elaborated in France, and there largely applied, 
give to science its accuracy and definiteness. In spite 
of this accuracy and definiteness, it is not immediately 
clear whether they will lead to completeness of know- 
ledge, or whether they may not be misapplied. To 
guarantee completeness, to make sure that in the whole 
great field no portion has remained untouched and un- 
explored, that love of detail, that searching and explor- 
ing spirit, is required which is nursed pre-eminently 
by historical and classical studies. And to avoid the 
abuse of existing methods, there is further required that 
critical spirit which inquires into the value of principles 


The exact, 
the histori- 
cal, and the 
habits of 



and the limit of their usefulness. These three directions 
of thought mark three tolerably distinct attitudes of the 
human mind. Skill in inventing and in applying new 
and precise methods — the exact habit or attitude of 
thought ; love of detail, and the desire for complete and 
exhaustive knowledge — the historical habit or attitude of 
thought ; lastly, the desire to become fully alive to the 
value of existing methods or principles, which implies a 
consciousness of the limited nature of one and every 
principle — the critical habit or attitude of thought. The 
progress of mathematics and natural science depends pri- 
marily on the first ; classical studies depend on the second ; 
philosophical reasoning mainly on the last. Each of the 
three nations which have led human progress and thought 
during the past centuries tias probably been possessed 
of these three cardinal virtues in equal proportions. For 
though Newton stands pre-eminent in the first, we have 
Laplace and Gauss and their numerous followers in other 
countries ; though the great volume of classical learning 
and criticism has emanated from the schools of Wolf, 
Hermann, and Bockh, they themselves point back to 
Bentley and Joseph Scaliger ; and even Kant's unrivalled 
enterprise was prepared by Hume, and dates back to 
Descartes. There need, therefore, be no angry rivalry or 
carping jealousy. We may point to the remarkably equal 
contributions of the three nations to the general progress 
of thought. But a very different and truly legitimate 
interest prompts us to note how in the great performances 
of each nation, in the literature of each of the three lan- 
guages, different factors have been at work — different 




agencies have combined to produce the effect. In this 
regard the spectacles presented by French, German, and 
English thought differ. And there seems to me little 
doubt that during a considerable portion of this century 
the German universities, grown out of theological, legal, 
and medical studies, and widening gradually till they 
embraced and deepened all three by the philosophical, 
the classical, and the exact spirit of research, present that 
organisation in which the different elements of thought 
are most equally balanced, through which modern know- 
ledge and the scientific spirit have been most widely 
and successfully diffused, and that the German ideal of 48. 

Tir' 1 J- ^ Til Combined in 

yVissensckaft embraces at once the highest aims of the the German 

'^ ^ ideal of Wis- 

exact, the historical, and the philosophical lines of ««"*«^A 

Nor would it be right to pass from the consideration of 
this peculiar feature of nineteenth-century thought, which 
is an outcome of the German university system, without 
noticing the moral significance which this ideal of Wvi- 44. 
senschaft acquired, and which marks it as a factor in oiwimn- 


progress and in culture of much more importance even 
than the lasting discoveries in science which it has made, 
or the monuments of learning which it has reared. It is 
not the political side of this movement which I refer to, 
not even pre-eminently the educational, though these are 
interesting and important enough to demand special his- 
torical treatment. What I should like to point to as the 
greatest in this movement is, that it belongs to the few 
and rare instances in the history of mankind when we 
see a large number of the most highly gifted members of 



a nation following a purely ideal cause, apart from the 
inducements which gain or glory may furnish. The pur- 
suit of truth and the acquisition of knowledge for its own 
sake, as an ennobling and worthy occupation, has during 
a large portion of our century been the life-work of pro- 
fessors and students alike in the German universities. 
In the biographies of many of them we meet with that 
self-denial and elevation of spirit which is the true char- 
acteristic of every unselfish human effort. In perusing 
these records of high aspirations, arising frequently amid 
disheartening surroundings, these stories of privations 
cheerfully endured, of devotion to an ideal cause, glow- 
ing with all the fervour of a religious duty, we gain a 
similar impression to that which the contemplation of the 
Classical period of Greek art or the early Kenaissance 
produces on our mind. 

Once at least has science, the pursuit of pure truth and 
knowledge, been able to raise a large portion of mankind 
out of the lower region of earthly existence into an ideal 
atmosphere, and to furnish an additional proof of the 
belief that there, and not here below, lies our true home. 
We may perhaps have to admit with regret that this 
phase is passing away under the influence of the utili- 
tarian demands of the present day ; we may be forced to 
think that another — and, we trust, not a lower — ideal is 
held up before our eyes for this and the coming age. 
But no really unselfish effort can perish, and whatever the 
duty of the future may be, it will have to count among 
the greatest bequests of the immediate past that high 
and broad ideal of science which the life of the Ger- 


man universities has traced in clear and indestructible 

^ The testimonies by illustrious 
foreigners to the great work of the 
German universities are frequent 
and well known, from the time 
when Mme. de Stael visited Ger- 
many, and her friend Villers wrote 
his * Coup-d'oeil sur les Universitds 
d'Allemague' in 1808, through the 
writings of Cousin, the verdict of 
Renan, of Cournot, of Dreyfus- 
Brisac, and of the American, J. M. 
Hart. To these often -repeated ex- 
pressions I will add that of the 
great apostle of higher culture of 
our age, of Matthew Arnold, who 
sums up his interesting report on 
the German system of higher edu- 
cation in these characteristic words : 
"What I admire in Germany is, 
that while there, too, Industrialism, 
that great modern power, is making 

at Berlin and Leipzig and Elber- 
feld most successful and rapid pro- 
gress, the idea of Culture, Culture 
of the only true sort, is in Germany 
a living power also. Petty towns 
have a university whose teaching 
is famous through Europe; and 
the King of Prussia and Count 
Bismarck resist the loss of a great 
savant from Prussia as they would 
resist a political check. If true 
culture ever becomes at last % 
civilising power in the world, and 
is not overlaid by fanaticism, by 
industrialism, or by frivolous pleas- 
ure-seeking, it will be to the faith 
and zeal of this homely and much- 
ridiculed German people that the 
great result will be mainly owing " 
('Schools and Universities on the 
Continent,' 1868, p. 256). 






The history of science in France and Germany during 
orgSiisation the first half of the present century is identical with the 

abroad. -^ x • j 

history of two great organisations, the Paris Institute and 
the German Universities. It is to them that we owe 


nearly all the great scientific work in the two countries : 
to the former we owe the foundation of the modern 
methods of scientific work during the last period of the 
eighteenth and the early years of the nineteenth cen- 
tury ; to the latter we owe pre-eminently the diffusion 
and widespread application of those methods.^ We now 
turn to the country which, in advance of France and Ger- 

^ In respect of this I cannot suf- 
ficiently recommend M. Maury's 
volume on ' L'ancienne Academic 
des Sciences,' which is as eloquent 
a testimonial to the scientific 
labours of eminent Frenchmen 
during the eighteenth century as 
the companion volume on ' L'an- 
cienne Academic des Inscriptions 
et Belles Lettres' is a proof of 
the absence of philological studies 
during that period. The recent 
publication of Lexis' work, *Die 
deutschen Universitaten,' is just 
as eloquent a testimonial to the 

labours of the German universities 
during this century. The first im- 
pression we get from the perusal of 
these two works is that for a long 
period France almost monopolised 
the exact sciences, just as later, 
for a similar period, Germany 
almost monopolised classical re- 
search, the science of antiquity. 
And yet the former was probably 
as much indebted to the English- 
man Newton as the latter was to 
the Frenchman Joseph Scaliger for 
the character each acquired during 
the two periods I refer to. 




many, had produced the greatest scientific model of modern 
times, a work which has probably done more than any 
other purely scientific work to revolutionise our scientific 
notions — the * Principia ' of Newton. In the subsequent 
history of the thought of this century, the next chapter 
will deal with the part that the Newtonian ideas have 
played throughout the whole period. We have now to 
turn our attention to the state of science in Great Britain 
during the period when Paris academicians and German 
professors combined to define and carry the spirit of 
modern scientific thought into the several mathematical, 
physical, and biological branches of research. 

Considering that the great scientific institutions of the 
Continent — the Paris Institute, the scientific and medical 
schools in Paris, and the German universities — have done 
so much for the furtherance of science and the diffusion 
of the scientific spirit, it is natural that we should ask, 
What have similar institutions done in this country ? „. .2. ; 

•^ Similar in« 

These institutions are, indeed, mostly older than the fn^oJ^^t'l^ 
academies and modern universities of the Continent. ^"^^°* 
The Eoyal Society, if not older than the French Academy, 
is certainly older than the Paris Academy of Sciences.^ 

^ The actual dates are as follows : 
The first Academy devoted to the 
pursuit of science seems to have 
been the "Aoademia Secretorum 
Naturae," founded at Naples in 1560. 
Several societies devoted to the cul- 
ture of lit«rature and art existed in 
Italy, such as the Academy " della 
Crusca" (founded at Florence in 
1582). The great French Academy, 
devoted exclusively to the study of 
the French language, dates from 
1629, and received its charter in 
1635. The Royal Society, though 

not the first scheme of its kind 
which was started in this country 
— for the establishment of a Royal 
Academy was discussed as far back as 
1616— actually started (1645) in the 
private meetings described in *Dr 
Wallis's Account of Some Passages 
of his own Life ' (quoted by Weld, 
* Hist, of the Royal Society,' vol. i. 
p. 30). These meetings, according to 
him, were suggested by a German, 
Theodore Hank, then resident in 
London. The members were " per- 
sons inquisitive into natural philos- 





The univereities of Oxford, Cambridge, Edinburgh, Dub- 
lin, and Glasgow ^ are older than most of the German 
universities which have done the great scientific work 
of this century. So far as wealth is concerned, no in- 
stitution on the Continent could compare with the two 
older English universities, and the Eoyal Society had 
in the beginning of this century long emerged from the 
poverty which characterised her early history during the 
lifetime of Newton.^ Let us look at the subject from a 

ophy, . . . and particularly of what 
hath been called the New Philosophy 
or Experimental Philosophy." It 
formed a branch at Oxford in 1649, 
and received a royal charter in 
1662, four years before the " Acad- 
^mie des Sciences " at Paris — which 
had also previously existed as a 
private gathering of savants at the 
houses of Mersenne, Montmort, and 
Thevenot — was formally installed in 
the Bibliothkiue du Roi. The 
" Accademia del Cimento " at Flor- 
ence was established in 1657 ; but 
it only lasted ten years. Very 
irregular were also the life and 
labours of the "Academia naturse 
Curiosorum" (later called A. 
Csesarea Leopoldina), founded at 
Vienna in 1652. The Accademia 
del Cimento printed an important 
volume of Transactions in 1666. 
The Royal Society published its 
first volume in 1665. The first 
volume of the 'Journal des Sa- 
vants ' is of the same year. Very 
complete information will be found 
on all foreign Academies in the 
'Grande Encyclopedie,' art. "Acad- 

^ Although the dates of the foun- 
dation of Oxford and Cambridge are 
uncertain, they were certainly more 
than a century — probably two cen- 
turies — older than Prague, the first 
German university, founded by the 
Emperor Charles IV. in 1347. The 

older Scotch universities were found- 
ed in the course of the fifteenth 
century, about the same time that 
Leipsic appears to have had its 
origin through a secession from 
Prague. The German universities 
— Halle, Gottingen — which were 
the seat of modem erudition, have 
a much later date, as given in chap, 
ii. p. 159, above. Edinburgh was 
founded at the end of the six- 
teenth century, and Trinity Col- 
lege, Dublin, about the same time. 
Leyden, which exerted a great in- 
fluence both on Scotch and German 
higher education during the seven- 
teenth century, was somewhat older 
than Edinburgh. 

2 It appears from Weld ('History,* 
&c., vol. i. pp. 231, 241, 246, 316, 462, 
473) that the financial position of 
the Royal Society was precarious, 
and frequently engaged the serious 
attention of the Council, during 
the whole first hundred years of its 
existence ; that as late as 1740 the 
whole revenue of the Society wa» 
only £232 per annum. An effort 
was then made to get in the large 
arrears of subscriptions and other 
contributions. In the following 
year the income seems to have 
exceeded the expenditure by £297. 
Weld adds, " It is a painful task to 
record these periodical visitations 
of poverty, which threatened the 
very existence of the Royal Society ; 

different point of view. England has during the early part 3. 
of the century, in all but the purely mathematical sciences, science in 

the early 

a greater array of scientific names of the first order than part of the 

" century, 

Germany, and nearly as great an array as France. Black, 
Herschel, Priestley, Cavendish, Davy, Young, Dalton, 
Faraday, Eowan Hamilton, Brewster, Lyell, Charles Bell, 
are all identified with one or more novel ideas or definite 
branches of research.^ Great Britain had thus no lack 

ous diflficulties, unassisted by Royal 
bounty and labouring alone on ac- 
count of their love for science " 
(vol. i. p. 474). 

there is, however, a proportionate 
amount of pleasure in witnessing 
the triumphant manner in which 
the small band of philosophers ex- 
tricated their institution from seri- 

^ The following are the principal dates referring to the great discoveries 
made in this country during the half -century ending 1825 : — 

1774. Priestley (1733-1804) discovers oxygen and a variety of other 


1775. Black (1728-99), Memoirs on latent heat. 

1775. Maskelyne (1732-1811) measures the Attraction of Mount She- 

1775. Landen (1719-90) expresses the arc of an hyperbola in terms of 

two elliptic arcs. 
1778. Benjamin Thompson (Count Rumford, 1753-1814) first experi- 
ments on heat by friction. 
1781, 13th March, Sir William Herschel (1738-1822) discovers Uranus. 
1784. Cavendish (1731-1810) discovers the composition of water. 
1786-97. Caroline Herschel (1750-1848) discovers her eight comets. 
1798. Cavendish determines the density of the earth. 
Davy (1768-1829), essay on heat, light, &c. 
Nicholson and Carlisle decompose water with the voltaic pile. 
Dalton (1766-1844), theory of evaporation. 
Young (1773-1829), first essay on the theory of light and colour. 
Dalton, law of expansion of gaseous fluids. 
Playfair (1748-1819), * Illustrations of the Huttonian Theory.' 
Wollaston (1766-1829), on Iceland spar, and undulatory theory. 
William Herschel, observations on nebulae and double stars. 


1802-3. Young expounds the principle of " Interference." 

1803-4. Dalton proposes the atomic theory. 

1804. Leslie (1766-1832), experiments on heat. 

1804. Wollaston discovers palladium and other kindred metals. 

1806. Davy isolates the alkaline metals. 

1807. Young introduces the word Energy (lect. i. p. 75). 

1809. Ivory (1765-1842), on the attraction of ellipsoids. 

1810. Young (in * Quarterly Review ') explains the different refractions 

in crystals. 
1810. Davy discovers chlorine to be a simple body. 




Alleged de« 
cline of 
science in 

either of great men of science or of great institutions, 
and yet — in spite of these — we read in the course of 
the first third of the century about the decline of 
science in England. That such could be seriously said 
of a country which within fifty years had in astronomy 
discovered a new planet (the first addition to the number 
known to the ancients), had discovered oxygen, latent 
heat, and the decomposition of water, applied the gal- 
vanic current for isolating the most refractory metals, 
laid the groundwork for the undulatory theory of light, 
established the atomic theory, put forth in statics and 
dynamics two of the most important modern generalisa- 
tions,^ and introduced in the treatment of electric and 

1810. Brown (1773-1858) publishes his * Prodromua Florae Novae Hol- 

landia),' &c. 

1811. Charles Bell (1774-1842) asserts the difference of sensory and 

motor nerves. 
1813. Brewster (1781-1868) begins his experiments on refraction and 

1813. Davy discovers iodine. 

1813. Wollaston publishes his synoptical scale of equivalents. 

1814. Wells (1757-1817), essay on dew. 

1815. William Smith (1769-1839) publishes his work on 'Strata.' 
1815. Brewster gives his law for determining the polarising angle. 

1815. Leslie (1766-1832) experiments on radiant heat and temperature 

of the earth. 

1816. Prout (1785-1850), Memoir on the position of hydrogen. 

1817. Young (in a letter to Arago) suggests transverse vibrations of 

1819. Kater (1777-1835) measures the length of the seconds-pendulum. 
1821. Faraday (1781-1867) discovers the rotation of a coil round a fixed 

1821. Brown, monographs on botanical subjects. 
1821. Sabine (1788-1883) experiments on the dip of the magnetic 

1823. Rowan Hamilton (1805-65) presents his paper on Caustics to- 

the Irisli Academy. 

1823. Faraday condenses chlorine and other gases. 

1824. Sir J. Herschel (1792-1871), observations of double stars. 

1825. Sir J. Herschel, on the parallax of fixed stars. 

^ The two important generalisa- the Application of Mathematical 

tions I refer to are contained in : Analysis to the Theories of Elec- 

1. George Green, *An Essay on tricity and Magnetism,' published 




magnetic phenomena novel conceptions, the value of 
which other fifty years have hardly sufficed to realise 
— is, indeed, an extraordinary fact well worthy of careful 
examination. Certainly the language in which Cuvier • 
with truth congratulates the French nation on the pre- 
eminence which it has attained in all branches of science 
contrasts strangely with the repeated attacks made in 
periodical literature, and in special pamphlets, on the 
state of science in England. And these not by persons * 
ignorant of the great names and signal achievements just 
mentioned, but by men of note, occupying all but the 
very first places among the scientific men of this country. 

It will suffice to give only two out of many examples 
of this criticism. 

One of the earliest complaints regarding the culture of 5. 
higher mathematics in this country will be found in an ofpiayfeir. 

at Nottingham by private subscrip- 
tion in 1828. The term " potential 
function," to denote the sum (F) 
obtained by adding together the 
masses of all the particles of a 
system, each divided by its distance 
from a given point, or in mathe- 
matical language V= f — > occurs 

there for the first time. See 
Green's mathematical papers, ed. 
Ferrers, 1871, p. 22. The function 
had before that time been used by 
Legendre and Laplace, but Green 
was the first to give a general 
mathematical theory of it. His 
essay remained unknown to the 
mathematical world, and the prin- 
cipal theorems were independently 
published by Gauss in his celebrated 
essay ' Allgemeine Lehrsiitze iiber 
die im verkehrten Verhaltnisse des 
Quadrats der Entfernung wirken- 
den Anziehungs- und Abstossungs- 
Krafte,' 1839. 

2. W. Rowan Hamilton's memoirs 
in the * Philosophical Transactions ' 
of 1834 and 1835, preceded by his 
theory of systems of rays in the 
'Transactions of the Royal Irish 
Academy,' 1828. In these papers 
is contained his celebrated prin- 
ciple of varying action, which is a 
development of Maupertuis's prin- 
ciple of least — or stationary — ac- 
tion. A great deal has been written 
on this principle, which is now con- 
sidered to be the most general 
principle of dynamics, as well for 
its mathematical usefulness in cal- 
culations (see Kirchhoff, ' Vorlesun- 
gen iiber mathematische Physik,* 
vol. i. pp. 28, 29), as from a phy- 
sical point of view (Helmholtz, 
in 'Journal fiir Mathematik,' vol. 
100). It has gained this import- 
ance since the conception of energy, 
or power to do work, has been 
placed at the base of the theory 
of all physical processes. 





excellent review of Laplace's ' M^canique celeste * by 
Playfair in the ' Edinburgh Eeview ' of 1808.^ " In the 
list of the mathematicians and philosophers to whom the 
science of astronomy for the last sixty or seventy years 
has been indebted for its improvements, hardly a name 
from Great Britain falls to be mentioned.^ . . . Nothing 
prevented the mathematicians of England from engaging 
in the question of the lunar theory, in which the interests 
of navigation were deeply involved, but the consciousness 
that in the knowledge of the higher geometry they were 
not on a footing with their brethren on the Continent. 
This is the conclusion which unavoidably forces itself 
upon us. . . . We will venture to say that the number 
of those in this island who can read the * Mecanique 
celeste ' with any tolerable facility is small indeed. If 
we reckon two or three in London and the military 

^ * Edinburgh Review,' vol. ii. p. 
279, &c. John Playfau- (1748-1819) 
was a native of Forfarshire, and 
Professor of Mathematics, and later 
of Natural Philosophy, at the Uni- 
versity of Edinburgh. "Playfair 
was struck with the backwardness 
of the English mathematicians in 
adopting the results of the Conti- 
nental analysts. While they boasted 
of Newton, they were unable to 
follow him, and the mantle of 
Newton had indeed passed over to 
France, where it rested ultimately 
on the shoulders of Laplace. Play- 
fair accordingly set himself to dif- 
fuse among his countrymen a know- 
ledge of the progress which science 
had been making abroad. This he 
did in a variety of ways, — by his 
articles in the ' Encyclopaedia Brit- 
annica,' by his papers in the Trans- 
actions of learned societies, by his 
articles in the * Edinburgh Review,' 
and by his class-teaching. As David 

Gregory introduced the Newtonian 
philosophy, so Playfair introduced 
the Continental methods into the 
studies of the University of Edin- 
burgh " (Sir A. Grant, * The Story 
of the University of Edinburgh,' 
vol. ii. p. 302). 

^ Playfair here excepts his country- 
man, Colin Maclaurin (1698-1746), 
' ' in whose time the teaching of 
mathematics at Edinburgh reached 
a point which it cannot be said to 
have yet surpassed" (ibid., vol. ii, 
p. 299 ; cf. also vol. i. p. 271, where 
a programme published in 1741 is 
given of the mathematical and phy- 
sical lectures at Edinburgh, which 
surpassed probably at that time 
the teaching of any other English 
or Continental university). Play- 
fair might have excepted also Ivory 
and the Englishman Landen, both 
of whom were well known among 
Continental mathematicians. 




schools in its vicinity, the same number at each of the 
two English universities, and perhaps four in Scotland, 
we shall hardly exceed a dozen, and yet we are fully 
persuaded that our reckoning is beyond the truth." 
The other opinion I am going to quote dates from more 

^ , & & U Babbage's 

than twenty years later, and is contained in a pamphlet by criticisms. 
Charles Babbage,^ who with Herschel and Peacock had 
done much to introduce at the University of Cambridge 
that knowledge of Continental mathematics which, accord- 
ing to the Edinburgh Eeviewer, was so much needed. His 
'Decline of the State of Science in England' (1830) was 
directed mainly against the Eoyal Society, as the review 

1 Charles Babbage (1792-1871), a 
native of Devonshire, well known 
all over Europe through his calcu- 
lating machine, was a very remark- 
able and original man. He lived 
during the age when the appli- 
cation of machinery to manufac- 
tures, trades, and arts produced 
the great reform in the industrial 
system of this country, and his 
talents, which might well have 
been employed in promoting pure 
science, were largely spent in solv- 
ing problems of practical interest. 
An account of these several pur- 
suits and schemes is given in his 

* Passages from the life of a Philos- 
opher,' London, 1864. Of his 
analytical machine we shall have 
occasion to speak hereafter (see p. 
248). Of the beginnings of the 
new school of mathematics at Cam- 
bridge he gives the following ac- 
count (p. 27). Having purchased 
for seven guineas a copy of Lacroix's 

* Diflferential and Integral Calculus,' 
he went to his public tutor to ask 
the explanation of one of his diflB- 
culties. " He listened to my ques- 
tion, said it would not be asked in 
the Senate House, and was of no 

sort of consequence, and advised 
me to get up the earlier subjects of 
the university studies." Repeated 
experience of this kind had the 
effect that he acquired a distaste 
for the routine studies of the 
place, and devoured the ' ' papers 
of Euler and other mathemati- 
cians scattered through innumer- 
able volumes of the Academies of 
Petersburg, Berlin, and Paris." He 
then perceived " the superior power 
of the notation of Leibniz." It 
being an age for forming societies 
for printing and circulating the 
Bible at Cambridge, Babbage con- 
ceived the plan of a society for 
promoting mathematical analysis, 
and to parody one of the many 
advertisements he proposed to call 
it a society for promoting "the 
Principles of pure d'lBm {d being 
Leibniz's symbol) in opposition to 
the dot-Sige {dots being Newton's 
notation) of the university." The 
most important result of this move- 
ment was the publication in 1816 
of a translation of Lacroix's treatise, 
and of two volumes of examples in 




of Playfair was against the English universities.^ " That 
science has long been neglected and declining in England 
is not an opinion originating with me, but is shared 
by many, and has been expressed by higher authority 
than mine."^ The author then proceeds to give ex- 
tracts from the writings of Davy, Herschel, and others 
on this subject. "It cannot," he says, "have escaped 
the attention of those who have had opportunities of 
examining the state of science in other countries, that 

^ Some of the causes of the de- 
cline as given by Babbage are in- 
teresting, the more so if we remem- 
ber that they were written at the 
period which marked the culmin- 
ation of Wissenschaft in another 
country (p. 10): "The pursuit 
of science does not in England 
constitute a distinct profession, as 
it does in many other countries. 
. . . Even men of sound sense and 
discernment can scarcely find means 
to distinguish between the posses- 
sors of knowledge merely elemen- 
tary and those whose acquirements 
are of the highest order. This 
remark applies with peculiar force 
to all the more difficult applications 
of mathematics ; and the fact is 
calculated to check the energies of 
those who only look to reputation 
in England." In 1794 Professor 
Waring of Cambridge wrote: *'I 
have myself written on most sub- 
jects in pure mathematics, and in 
these books inserted nearly all the 
inventions of the moderns with 
which I was acquainted ; . . . but 
I never could hear of any reader 
in England, out of Cambridge, who 
took the pains to read and under- 
stand what I have written ; " and 
" he then proceeds to console him- 
self under this neglect in England 
by the honour conferred on him by 
d'Alembert, Euler, and Lagrange" 

(see Todhunter, 'History of the 
Theory of Probability,' p. 453). 
•Babbage remarks (p. 13) that "in 
England the profession of the law 
is that which seems to hold out the 
strongest attraction to talent," that 
science is pursued as a favourite 
pastime, and that mathematics " re- 
quire such overwhelming attention 
that they can only be pursued by 
those whose leisure is undisturbed 
by other claims." "By a destruc- 
tive misapplication of talent we ex- 
change a profound philosopher for 
but a tolerable lawyer " (p. 37). 

'^ One of the causes given by the 
Edinburgh Reviewer of 1822 (vol. 
xxxvii. p. 222) is the following : 
' " In Cambridge there must always 
be a great number of men devoted 
to scientific pursuits ; but from the 
want both of the facilities and the 
excitements furnished by such an 
association, apt to lose the spirit of 
original investigation, — a remark 
peculiarly applicable to those young 
men who yearly distinguish them- 
selves in the favourite studies of 
the University, and who, after the 
laborious course of discipline by 
which they have attained the first 
object of their ambition, are prone, 
if left alone, to become the mere 
instruments for enabling others to 
pursue the same course." 


in England, particularly with respect to the more difficult 
and abstract sciences, we are much below other nations, 
not merely of equal rank, but below several even of 
inferior power." 

" It is," says the Edinburgh Eeviewer of 1816,^ " cer- • 
tainly a curious problem with respect to national genius, 
whence it arises that the country in Europe most gener- 
ally acknowledged to abound in men of strong intellect 
and sound judgment should for the last seventy or eighty 
years have been inferior to so many of its neighbours in 
the cultivation of that science which requires the most 
steady and greatest exertions of understanding, and that 
this relaxation should immediately follow the period when 
the greatest of all mathematical discoveries had been made 
in that same country." 

It must be said that these opinions, expressed as they 7. 

^ . Foreign 

were by men of the highest attainments, did not remain opinions on 
unchallenged at home or unnoticed abroad. It will be science, 
interesting to see how they have been met. Let us first 
hear what Cuvier says in his filoge of Sir Joseph Banks 
in 1821 2 regarding the work of the Royal Society during 
the period of forty-one years of his presidency : " During • 
this period, so memorable in the history of the human 
mind, English philosophers have taken a part as glorious 
as that of any other nation in those labours of the intel- 
lect which are common to all civilised peoples : they have 
faced the icy regions of both poles ; they have left no 
corner unvisited in the two oceans ; they have increased 
tenfold the catalogue of the kingdoms of nature; the 

* ' Edinburgh Review,' 1816, vol. ^ gee Cuvier, * l&loges historiques,' 

xxvii. p. 98. vol. iii. p. 79. 



heavens have been peopled by them with planets, with 
satellites, with unheard-of phenomena; they have counted, 
so to speak, the stars of the Milky Way : if chemistry has 
assumed a new aspect, the facts which they have furnished 
have mainly contributed to this change : inflammable air, 
pure air, phlogisticated air, are due to them ; they have 
discovered how to decompose water ; new metals in great 
number are the outcome of their analysis ; the nature of 
the fixed alkalis has been demonstrated by none but 
them-; mechanics at their call have worked miracles, and 
have placed their country above others in nearly every 
line of manufacture." Another foreigner. Professor Moll 
of Utrecht, remarked in his reply to Mr Babbage's 
pamphlet^: "If Mr Herschel and some of his friends 

^ The pamphlet was entitled ' On 
the alleged Decline of Science in 
England.' By a Foreigner. Lon^ 
don, 1831. It was by Dr Moll of 
Utrecht, and was introduced by a 
few lines from Faraday, who, with- 
out taking any side in the question, 
remarked that " all must allow that 
it is an extraordinary circumstance 
for English character to be at- 
tacked by natives and defended by 
foreigners." In the discussion on 
the subject by this writer, as also 
by Babbage, Herschel, Playfair, 
Whewell — pro and con. — a good 
many points of importance are 
brought out: some of them are 
still interesting, others refer to 
defects which have since been 
remedied. I will mention a few 
of them. Playfair, in the 'Edin- 
burgh Review' (vol. xxxi. p. 393, 
1819), thinks that the "very ex- 
tensive dissemination of general 
knowledge, which is so much the 
case over the whole of this king- 
dom," is against the advancement 
of the higher branches of mathe- 

* matics. This refers probably to 
the absence of periodicals devoted 
to special sciences, such as the 
* Annales de Chimie et de Physique,* 
published by Arago and Gay-Lussac 
' in France. In the absence of these 
special organs, memoirs of original 
value, which marked an era in 
special researches, were scattered 
in general literary reviews, as 
Young's on Light and Hieroglyphics 
in the 'Quarterly,' Herschel's and 
Airy's in the * Encyclopaedia Metro- 
politana ' ; and much good mathe- 
matics was buried in the ' Ladies' 
Diary ' among poetry of the " worst 
taste" and "childish scraps of litera- 
ture and philosophy " ('Edin. Rev.,' 
vol. ii. p. 282, 1808). Another 
point is that "the researches of 
English men of science have been 
too much insulated from each other 
and from what is doing in other 
countries" (Whewell to Vernon 
Harcourt, 1831 ; see Life by Tod- 
hunter, vol ii. p. 126). The British 
Association, which was founded very 
much as a result of this agitation, 



have such a poor opinion of the English scientific journals, 
a different judgment is entertained abroad, as is well 
proved by the eagerness with which the German journal- 
ists seize upon every article issuing from the presses of 
their British colleagues. The value which is set in 
Germany upon the scientific pursuits of the English, 
the rapidity with which translations are made in Germany 
of whatever English philosophers of some reputation pub- 
lish, shows abundantly that in that country at least, in 
docta Germania, a far greater value is set upon the pro- 
ductions of English science than is done by Mr Herschel 
and his friends." ^ 

has remedied this defect; and special 
periodicals exist now in multitudes ; 
but who could say that a third 
point has been sufficiently attended 
to — viz.f " the ignorance of foreign 
languages, which prevails both in 
England and in France : in Eng- 
land the number of those who 
acquire a smattering of French is 
very small, and still smaller is the 
number of those who know enough 
of German to read a book in 
that language without considerable 
trouble " (Dr Moll, loc. cit, pp. 7, 8). 
A fourth defect existing at that time 
is worth mentioning, as we have long 
left the age of such drawbacks ; it 
**is the high price in England of 
foreign books, in consequence of an 
importation duty." The paper 
duties were repealed in 1861. 

^ Moll, loc. ciL, p. 7. Another pas- 
sage is of interest, as bearing upon 
the difiference between the culture of 
science in England and in France : 
" At the time of the French Revolu- 
tion it so happened, by the exer- 
tions of d'Alembert, Clairault, Con- 
dorcet, and others, that of all 
sciences mathematics were the 
most fashionable. . . . With this 
view the Ecole Normale was 

founded, which, though of short 
duration, was perhaps of more 
utility towards the extension of 
mathematical 'knowledge than all 
the universities of Europe together. 
It was there that Laplace, La- 
grange, and Monge were lecturers, 
and men like Lacroix among the 
hearers. The study of classics 
having been in a great measure 
abolished by the French Revolu- 
tion, mathematics were studied in 
its stead ; and it thus happened 
that a number of mathematicians, 
unusually great, were scattered 
over the soil of France, and every 
one thought himself capable de 
faire les x, as they themselves 
called it, upon any given subject. 
But most of these investigations 
were all theoretical, and practical 
applications were foregone in almost 
every instance " (p. 11). " Mechan- 
ics in particular do not seem acces- 
sible, according to the tenets of the 
French school, to any man not well 
versed in sublime analysis. . . . 
Hence it arises that many have 
acquired a profound knowledge of 
the higher branches of mathematics, 
whilst the more elementary part of 
mathematics, which leads to the 




English re- 
plies to 

The answers to the challenges of Babbage and the 
Edinburgh Keviewer given by English writers them- 
selves cannot on the whole be said to be very reassur- 
ing. One of them counts the scientific periodicals in 
England and in France, but omits to weigh the merit 
of their respective contributions. Another points to the 
* Ladies' Diary/ in which many curious mathematical 
problems, far beyond the mere elements of science, are 
often to be met with. A third, whilst in general admit- 
ting the correctness of Babbage 's strictures, draws attention 
to the ' Penny Magazine ' and the ' Cabinet Cyclopaedia ' as 
counterparts in England of the Eeports of Cuvier and 
9. Berzelius abroad. The true position was probably recog- 
of the Brit- niscd bv the founders of the British Association tor the 

ish Associ- 
ation. Advancement of Science about 1830, who saw that, be- 

most useful applications, is far less 
diffused in France than in England" 
(p. 12). **The principle of the 
division of labour [in science] is 
more acted upon in France than in 
England" (p. 14). 

^ The movement, which origi- 
nated in the circle to which Bab- 
bage belonged, was — as stated 
above, p. 42 — to some extent 
copied from the German Associa- 
tion founded by Oken in 1822. The 
latter acquired a kind of European 
renown through the exertions of 
Humboldt in 1828, who succeeded 
in attracting a considerable number 
of celebrities — such as Gauss, Ber- 
zelius, Oersted t, — who for them- 
selves preferred a solitary to a " gre- 
garious " mode of science. Babbage 
was a guest at this meeting at Ber- 
lin, and gave an account of it in an 
appendix to the 'Decline of Science.' 
A good account of the character 
and gradually declining influence 
of these German meetings will be 
found in Bruhns' ' Life of Hum- 

boldt* (vol. ii. p. 127, &c., transla- 
tion). They " degenerated after the 
usual German fashion into the un- 
intellectual form of feasting." The 
British Association for the Advance- 
ment of Science, founded shortly 
afterwards on the 27th September 
1831 at York, was the immediate 
outcome of a suggestion thrown 
out by Brewster at the end of a 
review in the 'Quarterly' of Bab- 
bage's 'Decline of Science.' He 
fully endorsed the latter's opinion, 
and was even more severe upon the 
universities, maintaining " that the 
great inventions and discoveries 
which have been made in England 
during the last century have been 
made without the precincts of our 
universities. In proof of this we 
have only to recall the labours of 
Bradley, DoUond, Priestley, Caven- 
dish, Maskelyne, Rumford, Watt, 
Wollaston, Young, Davy, and Che- 
venix ; and among the living to 
mention the names of Dalton, Ivory, 
Brown, Hatchett, Pond, Herschel, 



sides a number of separate societies, " concentration was 
needed in one association in order to give more systematic 
direction to scientific inquiry, and that the first thing 
needed would be to procure reports on the state and the 
desiderata of the several branches of science." Babbage, 
at the Oxford meeting in 1832, "expressed the general 
feeling that meetings should be held in places likely to 
bring science into contact with that practical knowledge 
on which the wealth of the country depends." There is 
also no doubt that in the course of half a century the 
British Association has done a very extensive service 
to science in the direction of supplying the wants which 
its early founders clearly defined, and in bringing about 
that concerted action and scientific co-operation which so 
highly distinguishes the great academies and universities of 
France and Germany.^ It has done so without altogether 
destroying that peculiar feature which characterises not 
only the scientific but all the forms of the higher mental 
work of this country. In no country has the voice of 
public criticism been so free to unveil the shortcomings 
which attach to all — even the highest — human effort. In 
England there has existed for a long time the habit of 
promoting advance in every department by the cultiva- 

istics of 
higher men- 
tal work in 

Babbage, Henry, Barlow, South, 
Faraday, Murdoch, and Christie ; 
nor need we have any hesitation 
in adding that within the last fif- 
teen years not a single discovery or 
invention of prominent interest has 
been made in our colleges, and that 
there is not one man in all the eight 
universities of Great Britain who is 
at present known to be engaged in 
any train of original research" 
('Quarterly Review,' vol. xliii. p. 
327, 1830). He then suggests "an 

association of our nobility, clergy, 
gentry, and philosophers " (p. 342). 
^ The British Association has from 
the beginning had two features which 
did not exist in the German so- 
ciety — first, the Reports on the 
position of various branches of sci- 
ence, delivered by specialists of the 
highest ability ; and, secondly, the 
Committees, which undertake to 
do special work requiring concerted 




and univer- 
sities not 
always im- 

tion of party spirit, party criticism, and party shibbo- 
leths, as the easiest method of enlisting popular favour ^ 
and individual interest ; for here there exists no central 
authority which can create powerful organisations or dis- 
burse public means without the distinctly and repeatedly 
expressed support of a large section of the people. But 
all this must not induce us, in our historical survey, 
to dwell on the defects rather than on the excellence of 
the British contributions to the growth and the diffusion 
of science. Brilliant is undoubtedly the array of British 
names which have during the first half of this century 
become immortal by scientific labours, and it would be 
narrow-minded simply to emphasise the fact that they have 
not done so by the same means and through the same 
organisations as the Continental nations have established 
and perfected. For we must not forget that these even, 
with all their rightly extolled universality and breadth 
of spirit, have sometimes failed to recognise merit or to 
encourage genius. In spite of the impartial dealings of 
the Institute, on which Cuvier congratulates the French 
people, there are several instances in which contribu- 
tions of the first order lay unnoticed for many years. 

^ Referring to the British Asso- 
ciation itself, Charles Lyell wrote 
in 1838, after the Newcastle meet- 
ing, to Charles Darwin : " Do not 
let any papers, whether of saints 
or sinners, induce you to join in 
running down the British Associa- 
tion. I do not mean to insinuate 
that you ever did so, but I have 
myself often seen its faults in a 
strong light, and am aware of what 
may be urged against philosophers 
turning public orators, &c. But I 
am convinced, although it is not 
the way I love to spend my own 

time, that in this country no im- 
portance is attached to any body 
of men who do not make occasional 
demonstrations of their strength in 
public meetings. It is a country 
where, as Tom Moore justly com- 
plained, a most exaggerated im- 
portance is attached to the faculty 
of thinking on your legs, and where, 
as Dan O'Connell well knows, no- 
thing is to be got in the way of hom- 
age or influence, or even a fair share 
of power, without agitation " (* Life, 
Letters, and Journals of Sir C. Lyell,' 
London, 1881, vol. ii. p. 45, &c.) 



Fourier's great work on the theory of heat, which for the 12. 

_ . Fourier. ' 

first time propounded a universal method applicable to 
the mathematical treatment of almost every physical 
problem, inasmuch as it, so to speak, follows nature into 
the marvellous composition of the many movements out 
of which all her phenomena are compounded, lay buried 
for fourteen years in the archives of the Institute. That 
great authority had failed to recognise its paramount 
importance.^ Fresnel's first memoir, which established is. 

. Fresnel. 

on a firm mathematical basis the undulatory theory of 
light, was for years left unpublished, whilst the whole 
scientific world was anxiously expecting the results of 
his inquiries.^ In Germany we have examples of similar 

^ Jean Bapt. Jos. Fourier (1768- 
1830), of humble origin, in his 
celebi*ated 'Thdorie analytique de 
la Chaleur' (Paris, 1822), and in 
previous memoirs, carried further 
the mathematical treatment of phy- 
sical phenomena and introduced 
wider conceptions of mathematical 
quantities and their dependence — 
i.e.y of a mathematical "function." 
His investigations have led to far- 
reaching applications in physical 
science (Ohm and Lord Kelvin), 
and to profound mathematical theo- 
ries (Dirichlet, Riemann, &c.) The 
so-called "Fourier" series has thus 
a great applied as well as theoreti- 
cal interest. Fourier's first memoir 
was presented to the Institute in 
1807 ; an extract was published in 
1808 ; a second memoir was pre- 
sented in 1811 and crowned, but 
was not printed till 1824, two years 
after the great work itself had ap- 
peared. On the physical importance 
of Fourier's analysis see Helm- 
holtz, ' Vortriige und Reden,* vol. i. 
p. 101, &c. ; Sir W. Thomson, 
Mathematical and Physical Papers, 
passim, but especially vol. ii. p. 41, 

VOL. I. 

&c. On the purely mathematical 
interest that attaches to the Fou- 
rier series see especially Riemann, 
* Mathematische Werke,' p. 218, 
&c. A very concise summary of 
the history of the series is also 
given by George A. Gibson in the 
' Proceedings of the Edinburgh 
Mathematicat Society,' vols. xi. and 
xii. We shall revert to this subject 
in a subsequent chapter. 

2 Augustin Fresnel (1788-1827) 
divides with Thomas Young the 
merit of having established the 
undulatory theory of light on a 
firm basis. His first memoir on 
Diffraction of Light was presented 
to the Academy in 1815, a more 
extensive paper in 1818 ; this was 
crowned in 1819, but not printed 
till 1826. Other papers of his 
were mislaid or lost. The delay 
in bringing before the world these 
important discoveries has been at- 
tributed to the opposition of La- 
place and his party in the Institute, 
which even the influence of Arago 
could not overcome. See what Sir 
John Herscliel says in 1827, refer- 
ring to Fresnel's memoir of 1821 on 






discouragement and neglect being thrown in the way of 
the growth of new ideas. Pliicker of Bonn laboured for 
many years on the union of the geometrical and analytical 
methods in the treatment of geometry ; but he found so 
little appreciation that he abandoned his investigations, 
and only resumed them when in after-years a similar line 
of thought was independently developed in England.^ 

Transverse Vibrations, which the 
Academy had recommended to be 
printed : " We are sorry to observe 
that this recommendation has not 
yet been acted upon, and that this 
important memoir, to the regret 
and disappointment of men of sci- 
ence throughout Europe, remains 
yet unpublished" ('Ency. Metrop.,' 
article ** Light"). A full account 
of the opposition and difficulties 
which both Young and Fresnel 
had to encounter will be found in 
Whewell's * History of the Induc- 
tive Sciences,' vol. ii. In earlier 
times Reaumur seems to have ex- 
ercised a similar tyranny in the 
Academy of Sciences : see Maury, 
* Les Academies d'autrefois,' vol. i. 
pp. 280, 123; also Huxley, 'Critiques 
and Addresses,' 1890, p. 112, &c. 

1 Julius Pliicker (1801-68), pro- 
fessor at Bonn, equally known in 
England by his scientific co-opera- 
tion with Faraday and by that 
with Cay ley and Salmon, worked 
both in physics and geometry on 
independent lines. In the latter 
especially he brought about that 
union of purely geometrical and 
algebraic methods which has be- 
come so fruitful in the development 
of modern geometry and modern 
algebra. He had two periods of 
original geometrical work. The 
first began in 1826 (the year of 
the revival of mathematics in Ger- 
many), and closed in 1846. His 
mathematical researches were little 
noticed in his own country, where- 
as in France, and still more in 

England, his name was well known. 
After having published in 1846 a 
* System of Geometry,' which con- 
tained his former results in a more 
methodical form, he dropped his 
mathematical researches for twenty 
years, during which time he devoted 
himself to physical investigations of 
great originality. By these, if he 
had not been a personal friend, he 
might almost have been called a 
rival of Faraday (G. Chrystal in 
*Ency. Brit.') During a visit to 
England in 1864 he was agree- 
ably surprised to meet with ap- 
preciative interest from English 
geometricians, who had independ- 
ently worked on the same lines as 
he had done twenty years earlier. 
He was thus induced to resume his 
favourite studies, and to develop an 
idea which had already been expres- 
sed in his last-named work of 1846. 
This led to a new fundamental con- 
ception of geometrical forms, in 
which not the point but the line 
is the element of space. He was 
not spared to complete this line- 
geometry, but after his death his 
pupils found sufficient material to 
put his researches into a systematic 
form under the title, 'Neue Geo- 
metrie des Raumes, gegriindet auf 
die Betrachtung der geraden Linie 
als Raumelement' (Leipzig, 1868 
and 1869). See Clebsch on Julius 
Pliicker, Gottingen, 1872. A very 
appreciative notice of Pliicker, by 
George Chrystal, will be found in 
the 9th edition of the * Encyclopae- 
dia Britannica. ' 


Orassmann, in his ' Ausdehnungslehre/ published in 1844, 
is now generally admitted to have originated quite a novel 
way of considering geometrical relations.^ It took twenty 
years, however, before he succeeded in attracting any at- 
tention, and his great work, of which the first edition had 
been sold as waste-paper, was later on reprinted in its 
original form — mathematicians having now begun to study 
and recognise its intrinsic value. Such cases of neglect 
have undoubtedly been much more frequent in England, 
where even at the present day no central organisation 
exists which annually collects and arranges the scattered 
labours of individual workmen, and where that historical 
and encyclopaedic spirit is wanting which does its utmost 
to guarantee completeness and thoroughness of search 
and of research. Men of the greatest eminence, pioneers 




Central or- 
wanting in ' 

^ Hermann Grassmann (1809-77) 
was born, lived, and died at Stettin. 
He did not succeed till late in life, 
and fully thirty years after he had 
published his original investigations 
in geometry, in gaining for these the 
recognition and appreciation which 
they deserved. Neither he nor even 
Jacob Steiner at Berlin attained to 
positions worthy of their ability ; 
the latter, in spite of his connec- 
tion with other great mathemati- 
cians, never filled the chair of an 
ordinary professorship, whilst the 
former never entered the sphere of 
university teaching at all. The 
* Ausdehnungslehre,' as a new 
branch of mathematics, appeared 
in 1844. It is a science of pure 
extension, the application of which 
to empirical space is geometry. 
Similar investigations, in which 
space of three dimensions is con- 
sidered to be merely a particular case 
of pure extension of any number of 
dimensions, which are not neces- 
sarily determined by the same pro- 

perties as our empirical space, have 
become familiar since the publica- 
tion of Riemann's celebrated disser- 
tation of 1854 (published in 1867), 
and since Helmholtz was led to 
similar investigations by consider- 
ing the different dimensions or 
manifoldnesses of our sense per- 
ceptions (see his *Vortrage und 
Reden,' in many passages). Grass- 
mann, who at the end of his life 
witnessed the growing appreciation 
of his ideas, had filled up the in- 
terval with entirely different studies, 
the translation of the 'Rig- Veda' 
(Leipzig, 1876-77), and the compo- 
sition of a dictionary to the same 
(1872-75). He seems to have been 
the only mathematician, besides 
Thomas Young, who combined the 
ability for exact mathematico- 
physical and for philological studies. 
Both can complain of having been 
very insufficiently appreciated by 
their contemporaries. See Victor 
Schlegel, 'Hermann Grassmann,' 
Leipzig, 1878. 






in their line of thought and discovery, have to the present 
day remained popularly unknown to their countrymen, 
who have not only neglected but reviled them, allowing 
their great discoveries to be taken up as their own by 
foreicmers. Such was Dr Thomas Young, whom many 
educated persons at the present day cannot distinguish 
from the author of ' Night Thoughts.' ' The great founder 

1 Thomas Young (1773-1829), a 
native of Somersetshire, attained 
equal eminence by his discoveries 
in connection with the undulatory 
theory of light, in which he was 
the first to assert the principle of 
interference and that of transverse 
vibrations, and by his discovery 
of the key to the system of hiero- 
glyphics. Of his discoveries and 
suggestions some were published in 
anonymous review articles (so es- 
pecially his hieroglyphical papers) ; 
some in his Lectures on Natural 
Philosophy, delivered early in the 
century at the Royal Institution, 
and published 1807 ; some in the 
* Transactions of the Royal Society ' 
(from 1800 onwards) ; and some in 
various collective works, especially 
the ' Encyclopaedia Britannica.' The 
remarkable fact that Young, of 
whom Helmholtz says ('Vortrage 
und Reden,' vol. i. p. 279) that he 
came a generation too soon, re- 
mained scientifically unrecognised 
and popularly almost unknown to 
his countrymen, has been explained 
by his unfortunate manner of ex- 
pression and the peculiar channels 
through which his labours were an- 
nounced to the world. His fre- 
quently unintelligible style, his ob- 
scure and inelegant mathematics, 
the habitual incognito which he pre- 
served, his modesty in replying to 
attacks, and his general want of 
method in enunciating his ideas, con- 
trast very markedly with the writ- 
ings of some of his rivals, especially 

in France, where the qualities of 
style, method, and elegance were 
highly developed, and where recog- 
nised organs existed for the pub- 
lication of works of genius. The 
historian of thought, however, must 
not omit to state that several great 
names contributed, by the author- 
ity they commanded, to oppose 
Young's claims to originality and 
renown. Lord Brougham, shielded 
by the powerful anonymity of 
the ' Edinburgh Review,' and osten- 
tatiously parading the authority of 
Newton, submitted the views of 
Young to a ruthless and unfair 
criticism, the popular influence of 
which Young probably never over- 
came. The great authority on op- 
tics, Brewster, who has enriched 
that science by such a number of 
experiments and observations of 
the first importance, never really 
adopted the theories of Young and 
Fresnel. In the other great branch 
of research with which Young's 
name is now indissolubly connect- 
ed, in the science of hieroglyphics, 
the authority of Bunsen decided 
against Young and for the French- 
man ChampoUion. But this de- 
cision, which did so much to ob- 
scure the merits of Young, was 
founded on an insufficient know- 
ledge of the dates of Young's pub- 
lications. Since these were collect- 
ed by Leitch in the third volume 
of the ' Miscellaneous Works ' of Dr 
Young (London, 1855), the chrono- 
logy of his discoveries, which begin 

of modern chemistry, who next to Lavoisier did more 
than any one else to introduce into this science mathe- 
matical ideas, John Dalton, grew old and infirm before is. 

. . . naltoiu 

his countrymen sufficiently recognised and honoured him. 
Deprived of all but the very meanest apparatus for the 
proofs of his theories, and yet able to do what he did, 
what might not such a genius have accomplished if he 
had possessed the means of a Gay-Lussac or a Eegnault ? ^ 

in 1814, has been well established. 
See Benf ey, * Geschichte der Sprach- 
wissenschaft ' (Miinchen, 1869, p. 
729). Bunsen pronounced his ver- 
dict in his well-known work, 
* Egypt's Place in Universal His- 
tory,' published in 1845-57. On the 
whole, the words of Peacock, * Life 
of Dr Young' (London, 1855), p. 
472, are still correct : " His scien- 
tific works were rarely read and 
never appreciated by his contem- 
poraries, and even now are neither 
sufficiently known nor adequately 
valued ; whilst if justice was award- 
ed more promptly and in more lib- 
eral measure by his own countrymen 
to his hieroglyphical labours, these 
also were singularly unfortunate, as 
far as concerned the general diffu- 
sion of his fame, by coming into 
collision with adverse claims, which 
were most unfairly and unscrupu- 
lously urged in his own age, and 
not much less so by some distin- 
guished writers in very recent 

1 John Dalton (1766 - 1844), a 
native of Cumberland, spent the 
greater part of his life in teaching 
elementary mathematics at Man- 
chester, first at a college and then 
privately. In 1801 he propounded 
the law known under the joint name 
of Dalton and Gay-Lussac (who 
stated it six months later). In the 
years immediately following he ela- 
borated his atomic theory, which 
was to account for the existence of 

those definite quantitative relations 
between the chemical constituents 
of bodies known already to Richter. 
It was published in 1805. But the 
man who did most to make known 
to chemists the ideas of Dalton was 
Thomas Thomson (1773-1852), Pro- 
fessor of Chemistry at Glasgow, who 
in 1807, in the 3rd edition of his 

* System of Chemistry,' gave an ac- 
count of the atomic theory based 
upon communications of Dalton. 
Two memoirs published in the 

* Philosophical Transactions ' of 
1808 — one by Thomson on '* Oxalic 
Acid," and one by WoUaston on 
" Super- Acid and Sub-Acid Salts " 
— pointed to the great importance 
of the atomic theory, which (Wol- 
laston prophetically added) would 
not stop short with the determin- 
ation of the relative weights of 
elementary atoms, but would have 
to be completed by a geometrical 
conception of the arrangement of 
the elementary particles in all the 
three dimensions of solid exten- 
sion. The real merit of having ex- 
perimentally proved the theory of 
Dalton belongs to Berzelius, whereas 
Sir Humphry Davy opposed it for 
many years after it had been ac- 
cepted abroad. Dalton himself by 
no means followed the development 
which his ideas underwent at the 
hands of others. For example, he 
opposed Gay-Lussac's law of vol- 
umes. He was on the whole more 
successful in working out his own 








Faraday, instead of being backed by a wealthy Academy 
and ample assistance, had during all the years when his 
great discoveries were being made, to keep alive, with an 
income scarcely exceeding a hundred pounds a-year, an 
institution which but for him the memory even of such 
names as Eumford, Young, and Davy would not have 
sufficed to preserve from utter ruin and collapse.^ The 
author of one of the most suggestive treatises in the 
application of mathematics to physical phenomena, 
George Green, published it in 1828 at Nottingham by 
private subscription. Seventeen years later, William 
Thomson (Lord Kelvin) tried in vain to procure a copy 

ideas than in comprehending those 
of others who, like Berzelius, Mits- 
cherlich, Laplace, Liebig, and many 
later, contributed to the confirma- 
tion of the atomic theory. A good 
account of this is given in Henry's 
'Life of Dalton' (1854) and in 
Kopp's ' Entwickelung der Chemie 
in der neueren Zeit' (Miinchen, 

1 Michael Faraday (1791-1867), 
though not a mathematician, intro- 
duced into the science of electricity 
those ideas which have since been 
developed into a mathematical the- 
ory approaching in completeness the 
mathematics of the undulatory the- 
ory of light. What the atomic the- 
ory has done for chemistry, Fara- 
day's lines of force are now doing for 
electrical and magnetic phenomena. 
Dalton, though unacquainted with 
the higher mathematics of the 
French school, had essentially a 
mathematical or arithmetical mind. 
Faraday's peculiar ideas on the 
nature of electrical and magnetic 
action, though supported by an ex- 
perimental knowledge many times 
surpassing in volume and accuracy 
that of Dalton, did not find much 
appreciation among his contem- 

poraries. They were much more 
interested in his experimental re- 
searches than in his theories. In 
France andjltaly Faraday's eminence 
was recognised early. Already in 
1823 he was elected member of the 
Academies of Paris and Florence,, 
almost before any society at home 
had received him. "The circum- 
stances under which Faraday's work 
was done were those of penury. 
During a great part of the twenty - 
six years the Royal Institution was^ 
kept alive by the lectures which 
Faraday gave for it. 'We were 
living,' as he once said to the 
managers, 'on the parings of our 
own skin.' He noted even the 
expenditure of the farthings in 
research and apparatus. He hadl 
no grant from the Royal Society, 
and throughout almost the whole 
of his time the fixed income which 
the Institution could afford to give 
him was £100 a-year, to which the 
Fullerian professorship added nearly 
£100 more " (Bence Jones, * Life andl 
Letters of Faraday,' London, 1870^ 
vol. ii. p. 344). See also Bence 
Jones, 'The Royal Institution,,' 
p. 311. 

of this document, of which he knew by a reference in 
another work. At last he got possession of a copy which 
had probably during all this time been buried in the 
library of a prominent mathematical tutor at Cam- 
bridge, with whom he had been in frequent intercourse. 
Thomson then took it with him to Paris, where Sturm 
and Liouville at once recognised its merits. He then 
published it in * Crelle's Journal,' where it has ever 
since been referred to as a fundamental essay on the 
so-called potential theory.^ One of the most original 
thinkers on mathematics, who introduced a novel prin- 
ciple into algebraical science, George Boole, never at- ^n. 
tained to a higher position than that of teacher at a 
remote Irish provincial College.^ But perhaps the most 
signal example of the want of support which the 

1 See note 1 to p. 231 ; also Sir 
William Thomson, reprint of papers 
on "Electrostatics and Magnet- 
ism," 2nd ed., London, 1884, p. 2, 

note ; p. 126, note. 

2 George Boole (1815-64), a native 

of Lincolnshire, was one of the few 
gi-eat and original mathematicians 
who, like Leibniz and Grassmann, 
and to some extent Gauss, looked 
at the logical as well as the purely 
arithmetical side of the language 
of symbols. Though his treatises 
on 'Differential Equations' (1859) 
and on 'Finite Differences' (I860) 
have become well-known text-books, 
and his 'Laws of Thought' (1854), 
in which hg examined the found- 
ations of the mathematical theories 
of logic and probabilities, remains a 
unique work, his principal services 
to science lie in the direction of 
the "calculus of operations." In 
this branch of mathematics, which 
is peculiar to England, the sym- 
bols indicating an arithmetical op- 

eration are separated from those 
denoting quantity and treated as 
distinct objects of calculation. In 
connection with these investiga- 
tions, many of which have now 
penetrated into ordinary text- 
books, Boole was led to examine 
the conditions under which and the 
forms in which algebraical expres- 
sions, whilst undergoing changes 
and transformations, remain, never- 
theless, unaltered (invariant) (1841). 
By introducing this point of view 
he has, so to speak, created modern 
algebra; founding the extensive 
and fruitful science of "Invari- 
ants." Of this we shall treat 
later on. I now only refer to the 
further development of this sub- 
ject in the hands of Cay ley and 
Sylvester, and to the valuable 
sketch of the history of this branch 
of mathematics by Dr F. Mayer in 
the first volume of the 'Jahres- 
bericht der deutschen Mathemati- 
ker-Vereinigung,' Berlin, 1892. 





wealthiest of nations has shown to scientific genius is 
to be found in the history of Babbage's calculating 
engine. Yet this machine was approved by all experts 
— English and foreign — during the inventor's lifetime; 
and the Eeport of a Commission of the British Asso- 
ciation appointed specially to examine into the matter, 
concluded by stating that the scheme was perfectly feas- 
ible, and might, if carried out, mark an invention as great 
probably as that of logarithms.^ Who among us who 
has been interested in the promotion of institutions for 
higher education has not a story to tell of pecuniary 
troubles, continued through many a long year, whilst 
the wealth of the country seemed to exert its influence 
only in the direction of making the demands on a strug- 
gling establishment more formidable, the expenses more 
difficult to defray ? ^ 

^ On Babbage see p. 233, note 1. 
The history of the *' difference en- 
gines " and the " analytical engine " 
is given by Babbage himself in his 
'Passages from the Life of a Phil- 
osopher.' See also "Weld, ' History 
of the Royal Society,' vol. ii. p. 
369, &c. 

- Like the Royal Society, which 
for a century had to struggle 
with poverty, the Royal Institu- 
tion has a story to tell of want 
of funds through a long period of 
its early existence. See Bence 
Jones, 'The Royal Institution,' 
London, 1871, pp. 202, 281. The 
Royal Institution was founded by 
Benjamin Thomson, Count Rum- 
ford (1753-1814), and had origin- 
ally not a scientific, hardly even a 
higher educational object. The 
scheme arose in the mind of its 
founder after he had successfully 
exerted himself at Munich under 
the patronage of the Elector of 

Bavaria in founding industrial work- 
houses, improving the state of the 
army, and putting down beggary 
and immorality in the capital and 
country. His principle was to 
make " vicious and abandoned 
people first happy and then virtu- 
ous" (p. 31). After leaving Mun- 
ich in 1793 and spending two years 
in Italy, similarly occupied, he 
visited London in 1795 in order to 
publish his Essays, which appeared 
separately between 1796 and 1802. 
The first essay contained " a pro- 
posal for forming in London by 
private subscription an establish- 
ment for feeding the poor and giv- 
ing them useful employment, . . . 
connected with an institution for 
introducing and bringing forward 
into general use new inventions 
and improvements," &c., &c. (p. 
44). The first outcome of this was 
the formation of a society for en- 
couraging industry and promoting 



But it is hardly the duty of the historian of thought to 
record that which belongs more to the impediments of 
mental progress than to its promotion, were it not that 
in and through these peculiar circumstances the genius 
of the nation has developed its main features, its strong 
character. These are manifest as much in the depart- 23. 


ment of science as they are in general literature and in isticsof 

•^ o English 

the institutions of practical life. British science through thought. 
all the centuries, since the time of Eoger Bacon, and 
in spite of the efforts of his illustrious namesake, has 

the welfare of the poor. William 
Wilberforce was one of the original 
promoters ; Thomas Bernard, the 
founder of many other charitable 
institutions, one of its most active 
members. To a committee of this 
Society Count Rumford submitted, 
in 1799, his proposals for forming 
the Royal Institution, and it was 
accordingly founded in February of 
that year on private subscriptions 
of fifty guineas each. It was de- 
scribed as a "public Institution 
for diffusing the knowledge and 
facilitating the general introduc- 
tion of useful mechanical inven- 
tions and improvements, and for 
teaching by courses of philosophical 
lectures and experiments the appli- 
cation of science to the common 
purposes of life." In the course of 
a very few years the original char- 
acter of the Institution entirely 
changed, the aim of influencing 
directly the condition of the poor 
was lost sight of, and little re- 
mained besides the result of " bring- 
ing science into some degree of 
fashion " and " affording a new em- 
ployment and amusement to the 
higher classes of life." The inter- 
est of the Institution for the his- 
tory of thought is the fact that in 
its laboratory Davy and Faraday 

conducted their researches, and that 
they, as well as Young, Coleridge, 
and Sydney Smith, there delivered 
their lectures. And the history of 
the Royal Institution is also typical 
of the history of other establish- 
ments for higher culture in this 
country : it has been in its main 
features repeated on a larger or 
smaller scale in many provincial 
societies, and notably in the col- 
leges of Manchester, Birmingham, 
Liverpool, Newcastle, Leeds, Bris- 
tol, Nottingham, &c. Started by 
persons with large but nevertheless 
insuflBcient means, or by subscrip- 
tions and endowments of moderate 
extent, obliged to gain popularity 
and fashionable support in order to 
meet their growing expenses, these 
institutions have depended mostly 
on individual energy for their first 
successes, and have all had to pass 
through periods of great difl&culty, 
till in course of years they have 
acquired a special character of use- 
fulness and defined their peculiar 
sphere of action. The absence of 
a definite programme and a great 
waste of energy and funds over 
special departures are not un- 
common features of these develop- 

Absence of 
schools of 
thought. ■ 



refused to congregate in distinct schools and institutions 
or to be localised in definite centres. The Eoyal Society, 
the Eoyal Institution, the British Association, and many 
other smaller societies, have all more or less started with 
the programme of Lord Bacon, and have failed to realise 
it : everywhere the schemes of co-operation or organised 
scientific research have encountered the opposition of 
individual pursuits or of local interests. 

Newton could not secure the use of Flamsteed's obser- 
vations, which on their part remained uncompleted and 
unpublished through the want of appreciation of others. 
Great schemes in practical life have been carried out 
by the unaided efforts of eminent persons, and great 
ideas have been put forward with all the power and 
all the resources of individual genius,^ but no great 
master in scientific research in this country can point 
to a compact following of pupils — to a school which 
undertakes to finish what the master has begun, to carry 
his ideas into far regions and outlying fields of research,, 
or to draw their remoter consequences. Newtonianism 
was a creation of Voltaire ; the school of Locke is to be 
found in France ; the best realisation of Bacon's schemes 
are the EncyclopMie, the French Institute, and the 
foreign Academies.^ Dr Young's discoveries in optica 

^ See Huxley, 'Lay Sermons, 
&c.,* edition of 1891, p. 43 : "Eng- 
land can show now, as she has been 
able to show in every generation 
since civilisation spread over the 
West, individual men who hold 
their own against the world, and 
keep alive the old tradition of her 
intellectual eminence. But in the 
majority of cases these men are 
what they are in virtue of their 

native intellectual force, and of a 
strength of character which will 
not recognise impediments. They 
are not trained in the courts of 
the Temple of Science, but storm 
the walls of that edifice in all sorts 
of irregular ways, and with much 
loss of time and power, in order to 
obtain their legitimate positions." 
2 See above, pp. 34, 95. 



and hieroglyphics were made known to the learned world 
through his French contemporaries. Dalton,^ Charles 
Bell,^ Faraday, Darwin, and Maxwell, no less than 
Bentley and Gibbon,^ have furnished the text for lecture- 
courses in German universities, and created a whole 
literature of pamphlets and scientific memoirs.* English 
societies may sometimes honour and admire, but they do 
not support, their great representatives, and these them- 
selves often refuse to be tied by exclusive academic 
duties, still more by official restrictions. Two charac- 
teristics have marked most of them : they have, at all 
expense and sacrifice, guarded their individual freedom 25. 

_ Individual 

of thought, and they have almost always shown a great character 

^ ' "^ "^ ° andpracti- 

desire to combine some application with their abstract ^En°uX^ 
researches, to take part in the great practical work of 
the nation. Continental thinkers, whose lives are devoted 
to the realisation of some great ideal, complain of the 
want of method, of the erratic absence of discipline, which 
is peculiar to English genius. The fascination which 
practical interests exert in this country appears to them 
an absence of full devotedness to purely ideal pursuits.^ 


^ See above, p. 245, note. 
2 See above, p. 193, note. 

* See above, p. 169, note. 

* Germany may be said to have 
produced Darioinismus in this cen- 
tury aa France created Newtonian- 
isme in the last. Huxley writes 
(*Life of Darwin,' vol. ii. p. 186) : 
"None of us dreamed (in 1860) 
that in the course of a few years 
the strength (and perhaps I may 
add the weakness) of Darioinismus 
would have its most extensive and 
most brilliant illustrations in the 
land of learning." Quite recently 
Prof. Boltzmann at Munich, and 
M. Poincar^, have published courses 

of lectures on Maxwell's electric 

^ What appears irksome to an 
English genius — the red tape of 
academic restrictions, the barriers 
of officialism, and the duties of the 
teacher — melted away in the glow 
of enthusiasm and love of truth 
which animated the great leaders 
and founders of university culture 
abroad ; as Goethe has told us that 
the rigid form of the sonnet melts 
in the fervour of the love-song : 

•' Das Allerstarrste freudig aufzuschmel- 

Muss Liebesfeuer allgewaltig gliihen." 

— Sonette No. 14. 






English pe 
more pro 

part of the 

The English man of science would reply that it is unsafe 
to trust exclusively to the guidance of a pure idea, that 
the ideality of German research has frequently been 
identical with unreality, and that in no country has so 
much time and power been frittered away in following 
phantoms, and in systematising empty notions, as in the 
Land of the Idea ; but he would as readily admit that 
his own country is greatly deficient in such organisations 
for combined scientific labour as exist abroad, and that 
England possesses no well-trained army of intellectual 

These differences between English and Continental 
science were most pronounced in the first half of the 
dSS*^^ri present century, when Germany developed her university 
system, when France clearly defined the exact scientific 
methods, and when the encyclopaedic view — peculiar to 
the historical and philosophical pursuits of the earlier 
years — gradually became dominant in the exact sciences 
also. Since then the intercourse of the different nations 
has done much to destroy these national peculiarities. 
The reform of the universities, in which Germany was 
engaged in the early years of the century, did not touch 
the English universities before the middle of the century. 
In the meantime quite different demands had sprung up 
all through the civilised world ; and as nothing repeats 
itself in history, it will be impossible to reach in this 
■country the same broad organisation for purely intellec- 
tual work as Germany can rightly boast of during the 
period we are dealing with. Some persons doubt whether 
it will be maintained in Germany. It appears still more 
doubtful whether such an organisation could now be 

created in the face of the industrial spirit of our age. Ever 
since the latter half of the eighteenth century schemes for 
a general education of the masses have attracted the 
thought and the attention of philanthropists and states- 
men in many countries of Europe. But the directions 
taken by these educational efforts have been character- 
istically different in the different countries, and their suc- 
cess, so far as the great masses of the people are con- 
cerned, has been very partial indeed. It is true that 
during the first thirty years no country possessed such 
distinguished schools of science as did France in the great 
scientific and medical institutions of her capital. It is 
also true that no country equalled Germany in her system 
of universities and higher schools, which had come under 
the influence of classical learning and philosophical ideals. 
England, which at that time took no part in the educa- 
tional movements of the Continent,^ possessed, neverthe- 

^ This statement requires two 
qualifications. Firstly, both Milton 
and Locke have had great influ- 
ence in spreading enlightened views 
regarding the principles and the 
object of education in general — 
especially in the direction of en- 
larging the idea of education, so as 
to make it comprise something more 
than merely instruction and pedan- 
tic teaching. I cannot find, how- 
ever, that in England, either in the 
direction of higher university edu- 
cation or of a general system of 
popular education, their influence 
has been very marked. Locke's 
influence abroad, through his psy- 
chological analysis of the mind, has 
been very considerable. Secondly, 
in the direction of practical educa- 
tion, of the endeavour to reach 
large numbers of the people by 
educational institutions, we must 

look with admiration to the early 
work done in Scotland, which in 
this respect somewhat resembles 
Switzerland. The Scotch system of 
parochial schools, and their influence 
on the education of the people, 
has been too little studied abroad, 
though rightly extolled at home. It 
is true that, with the exception of 
Calvin, none of the great Continen- 
tal educationalists— such as F^ne- 
lon, Rousseau, Pestalozzi, or W. 
von Humboldt — have had any di- 
rect influence on Scotland ; nor has 
the educational work of Scotland 
produced any great educational 
literature like that which Switzer- 
land can boast '.of, and which has 
brought the theory of education 
so prominently before the world. 
But nevertheless there it stands, 
this creation of John Knox and 
the early Reformers. "Civilised 






less, something peculiar in her two great universities, 
character of It was neither the scientific, nor the classical, nor the 

English uni- 
versities, philosophical spirit exclusively which reigned there ; if 

any or all of them had ruled, we should not meet with 

those repeated complaints that higher mathematics were 

absent in Cambridge, that no philological studies were 

cultivated in either of the universities, and that philosophy 

was represented merely by Aristotle, Butler, Locke, and 

Paley.^ According to the representatives of the university 

Europe has never witnessed a nobler 
spectacle than the first Protestants 
of Scotland in the assembly of the 
nation demanding that from the 
funds before abused by a licentious 
superstition one - third should be 
devoted, not to increase the rev- 
enue of the Reformed Church, but 
to the education, the universal edu- 
cation, of the youth in all depart- 
ments of instruction, from the high- 
est to the lowest" ('North Brit. 
Rev.,' 12, p. 483). 

^ As to the deficient mathemati- 
cal teaching at Cambridge, see p. 
233, note, &c. The complaints re- 
garding the teaching of other sub- 
jects are frequent, but belong to a 
later date, the middle of the century, 
when the Royal Commission of In- 
quiry, which was appointed under 
the Government of Lord John Rus- 
sell on the 31st August 1850 and 
expired with the presentation of its 
report on the 30th August 1852, 
attracted the attention of the pub- 
lic to university reform, and gave 
rise to a very full discussion of the 
whole subject in the various liter- 
ary papers and reviews. The two 
older universities are called "cita- 
dels of political prejudice and sec- 
tarian exclusiveness, instead of be- 
ing the temples of liberal arts and 
the repositories of science" ('Brit. 
Quart. Review,' 1860, July, p. 205). 
Theology is stated to be * ' the last 

thing taught at Cambridge " (ibid. , 
p. 221); there was no professor of 
Latin, none of English literature, 
of logic and metaphysics, of modern 
languages (p. 225). In 1849 Cam- 
bridge had no laboratory ; the uni- 
versities took no part in the legal 
training of lawyers ('Edin. Rev.,' 
April 1849, p. 511) ; Oxford afforded 
no training in natural science (ibid.) 
Cambridge " sacrificed to the mon- 
opoly of a severe geometry every 
other exercise and attainment of 
the human mind. There was no 
theological study, no study of his- 
tory, none of moral science, none of 
chemistry, none even of experi- 
mental philosophy" (ibid., p. 514). 
These criticisms were fully justified 
by the Reports of the Commissions 
published in 1 852. See on the teach- 
ing of Theology at Cambridge, Re- 
port, pp. 89, 102 ; Evidence, pp. 88, 
168, 190, 216 : on the teaching of 
Latin, Rep. , pp. 98, 102 ; Evid., pp. 
165, 176, 289 : on the teaching of 
English, Evid., pp. 124, 136 : of mo- 
dern Languages, Rep., pp. 26, 101 ; 
Evid., pp. 16.5, 216, 300: of Law, 
Rep., pp. 35, 182 ; Evid., pp. 123, 
190 : of Natural Sciences, Evid., p. 
115, &c. In 1874 the 'Edinburgh 
Review ' could point out that during 
twenty years, whilst the examination 
for the Indian Civil Service had been 
thrown open, the English universi- 
ties had practically contributed no 



system, what England did possess was the ideal of a liberal 28. 
education. But none of these three forms of intellectual Liberal Edu- 


training — neither the scientific in Paris, nor the classical 
in Germany, still less the liberal in England — touched 
the great masses of the people. They all did good work 
in their respective lines ; but they left, or would by them- 
selves have left, the country in darkness. The begin- 
nings of general popular education are to be traced 
independently in Switzerland, in Scotland, and in many 
of the small States of Germany.^ The great scientific 

candidates to the competition (April 
1874, p. 342). " Nothing about uni- 
versity life was more striking" to 
the Edinburgh Reviewer "than the 
contrast between the efforts and 
the high aims of the few, the 
culture and solid result achieved 
by them — and the utter uselessness 
of it to the many " (p. 354). The 
* Quarterly Review ' of June 1826 
notes '* a growing taste for the 
cultivation of physical science as 
characteristic of the state of the 
public mind in England" (p. 159), 
and refers to the " measures which 
have been carried into efiect 
throughout the country with great 
harmony of design, although chiefly 
by the unassisted exertions of pri- 
vate individuals, . . . the recent 
establishment of numerous literary 
and philosophical institutions in our 
metropolis and many of our pro- 
vinces " (ibid., p. 154). 

^ The great Reformers — Luther, 
Melanchthon, Zwingli, and Calvin — 
alike took a great interest in educa- 
tion, which they intended to be uni- 
versal and popular. But their suc- 
cess, so far as the education of the 
people was concerned, remained 
everywhere very partial. A real or- 
ganisation of primary schools was 
not attained. They prepared for 
it by introducing the vernacular 

languages, the reading of the Bible, 
the popular hymns. Their main 
efi'orts lay in the training of good 
teachers for church and schools in 
the reorganisation of what were 
called the Latin schools. In the 
course of the sixteenth and seven- 
teenth centuries the smaller Protes- 
tant States of Germany — especially 
Saxony, Wiirtemberg, Brunswick, 
the northern cities Hamburg and 
Liibeck — received under various 
forms what was called " Eine Kir- 
chen- und Schuiordnuug." Luther's 
tract of the year 1524, addressed 
to the " burgomasters and coun- 
cillors of all towns of the German 
land, that they should found and 
maintain Christian schools," was 
the beginning of this movement. 
In Scotland burgh schools, also 
grammar (or Latin) schools and 
lecture schools, "in which the 
children were instructed to - read 
the vernacular language," existed 
long before the Reformation. But 
to John Knox is due the scheme 
for popular education contained in 
the ' First Book of Discipline.' The 
parochial schools were started in 
many instances by voluntary or ec- 
clesiastical assessment through the 
efforts of the Reformed clergy. 
The foundation of the subsequent 
system of parochial schools was laid 



schools of France trained the civil and military engin- 
eers in that country, and produced text- books for the 

in the statute of 1696. It must 
not be forgotten, however, that the 
*' Order of Jesus " (founded 1540), 
whose higher educational work lias 
found so much appreciation from 
men like Sturm — the Protestant 
educationalist — Lord Bacon, and 
Descartes (see the quotations in 
Schmidt's ' Geschichte der Piidago- 
gik,' 4th ed., vol. ii. p. 248), was also 
active in the direction of popular 
and primary education. In emula- 
tion of the Protestant movement, 
it had introduced "school regula- 
tions " in many Catholic countries, 
and even founded a special order 
— the "Patres piarum scholarum" 
(1600) — for the education of the 
poorer classes (ibid., p. 253). Whe- 
ther the statute of 1696 is the ear- 
liest official document referring to 
popular education and providing the 
means of maintaining an adequate 
number of schools (one in 1000 of 
population) to teach the lower 
classes, I cannot say. It appears 
that Duke Ernest of Gotha, in the 
course of the seventeenth century, 
established a general system of 
primary education in his terri- 
tory which was ' * quite unique, at 
first ian object of ridicule, but then 
very soon of emulation" (ibid., p. 
333). The regulations were cer- 
tainly most wise and liberal, and 
attendance was made compulsory. 
The question of popular education 
was taken up on a much larger 
scale by Frederick the Great in the 
middle of the eighteenth century. 
The year 1763, which marks the 
end of the Seven Years' War, is 
also the year of an edict which 
forms the basis of the regulation 
of popular education for the whole 
monarchy : it establishes village 
schools with compulsory attend- 
ance. It met with much opposi- 
tion, and its ends were only slowly 

realised, and only as training-schools, 
where a sufficient number of teach- 
ers were educated, sprang up, and 
as popular school and story-books 
were provided. Campe, with his 
edition of ' Robinson Crusoe,' marks 
an epoch in this direction. In fact, 
the cause of universal popular edu- 
cation remained in the hands of 
private persons, frequently of men 
of great insight and organising 
ability — such as A. H. Fran eke 
(1663-1727), the indefatigable friend 
of the poor and of orphans ; Base- 
dow (1723-90), the founder of the 
Philanthropin and populariser of 
Rousseau's ideas ; Von Rochow 
(1734-1805), the friend of the coun- 
try-folk and founder of village 
schools; Von Felbiger (1724-88), 
the adviser of Maria Theresa and 
Joseph II., the organiser of the 
popular educational system in Aus- 
tria (1770-80) : or else it was de- 
pendent on the casual favour of 
enlightened princes and sovereigns. 
At length, in the middle of the 
eighteenth century, training-schools 
for teachers, so-called "seminaries," 
were founded all over Germany. A 
beginning had been made by Duke 
Ernest of Gotha (1601-75), but 
had been neglected like many 
other beginnings. But in the 
second half of the eighteenth cen- 
tury no less than thirty-three semi- 
naries were founded all over Ger- 
many, including Austria. For details 
on this important and interesting 
subject, see the third volume of 
Schmidt's 'Geschichte der Pada- 
gogik. ' Freytag's ' Bilder aus der 
deutschen Vergangenheit ' also con- 
tains many interesting details ; but 
above all I would recommend for 
the countries of the west and south 
of Germany the valuable reaearchea 
of C. T. Perthes contained in his 
' Politische Zustande und Personen 


•^higher scientific training of the whole of Europe ; ^ but 
no serious effort was made, during the brilliant days of 
the First Empire, to secure for the nation the blessing of 
a popular education. This state of things continued 
under the Eestoration ; the real beginnings of an or- 
ganised primary system are to be found in Guizot's 
celebrated law of 1833. In Germany the influence of 
Pestalozzi and Zschokke in the south; of Basedow, Francke, 
and the school of Kant and Herder, and, later, of Herbart 
in the north, — stimulated many Governments to establish 
a system of popular schools for the education of the masses, 
and a system of seminaries for the training of a popu- 
lar teaching staff. This movement was chiefly carried 
on independently of the reform of the universities and 
higher schools, over which the ideal of Wissenschaft ex- 
ercised a powerful spell. Under the latter were trained 
the leaders and higher teachers of the nation, as well as 
the members of the learned professions. The educational 
influence of this ideal on the more gifted among the 
student class was the very highest and best ; but it hardly 

in Deutschland zur Zeit der fran- 
zosischen Herrschaft,' 2 vols., Gotha, 
1862 and 1869. As unfortunately 
this work, with its collection of 
interesting and not easily accessible 
facts referring to the inner history 
of the German people, has no index, 
I give the following references : 
Compulsory education in Kur Trier 
in 1712, vol. i. p. 225 ; in Kurmainz, 
1750, vol. i. p. 19 ; popular educa- 
tion in Baden, vol. i. p. 411 ; in 
Bavaria, vol. i. pp. 436, 467 ; in 
Wiirtemberg, vol. i. p. 637 ; and the 
chapter on Joseph II. 's school re- 
form, vol. i. pp. 153-170. The sem- 
inary or training-school being thus 

VOL. I. 

the centre and beginning of na- 
tional education in Germany, as it 
has also, with a different constitu- 
tion, become the centre of scientific 
work (see p. 214, note), it is inter- 
esting to note that Scotland, so far 
advanced in educational work, had 
no real training-school for teachers 
before Stow started his Normal 
School in Glasgow (see 'Cham- 
bers's Encyclopaedia,' art. "Educa- 
tion"), and that the "seminary" 
for higher scientific work has to 
this day not yet been introduced 
into this country. 

^ See above, p. 44, note. 




Union of 
and instruc- 

reached the multitude of less gifted minds, who always 
gave themselves to bread-studies ; and it must necessarily 
fail yet more when not only the future teachers and 
leaders, but the masses of the nation, flock into the halls of 
the universities. Imperceptibly a differentiation has taken 
place in Germany between the educational work which 
was meant to reach the people at large and the intellectual 
instruction of a select few. But it is exactly this differ- 
entiation of education and higher instruction which the 
champions of a liberal education in England have desired 
to avoid.^ In France, very soon after Kousseau's time, dis- 

1 The two developments in Ger- 
many start from different centres. 
The purely educational movement 
began in Switzerland with Pestal- 
ozzi (1746-1827). His forerunner 
was Martin Planta (1727-1772), his 
successors were legion, all over 
Europe, including sovereigns, states- 
men, and philosophers. He created 
an enthusiasm for education, which 
was to begin at home, not in the 
school ; to depend on the influence of 
the mother ; to be founded on a re- 
ligious spirit ; to direct itself to the 
development of the body as much as 
of the mind ; to rest primarily on ob- 
servation and experience, not mainly 
on memory and learning ; and then 
to absorb the whole mind and the 
entire man, not exclusively the in- 
tellect. It was to begin from be- 
low, not from above, with the 
people, the poor, the unfortunate 
and deserted ; on the part of the 
teacher it was to be a sacrifice, 
an end in itself, not a profession. 
The greatest followers of Pestalozzi 
were Von Fellenberg (1771-1844), 
the founder of Hofwyl and other 
industrial schools for poor and de- 
serted children among the peasant 
population of Switzerland; Johan- 
nes Falk (1760-1826), the founder 

of a great number of houses for the 
poor and the fallen, of the "So- 
ciety of Friends in Need " ; J. H. 
Wichern (1808-1881), the founder 
of the "Rauhe Haus" near Ham- 
burg ; lastly, the celebrated Frobel 
(1782-1852, a native of Thiiringen)^ 
the founder of the Kindergarten. 
The other — not to say opposite — 
development was centred in F. A. 
Wolf, in whose school the ideal of 
Wissenschaft with its enormous in-^ 
fluence on universities and high 
schools was elaborated. In the 
history of this development, with 
which our second chapter dealt, 
the name of Pestalozzi does not 
occur. The term "popular" was 
for a time banished as identical 
with the ^avavffla of the ancient 
Greeks. The two movements find 
a connecting-link in the extra-aca- 
demical, the classical literature of 
Germany, notably of Herder and 
Goethe,* to whom we must add 
Fichte and Schleiermacher. The 
present age is working towards 
a fusion of both interests, of the 
educational and higher scientific, 
the bridging over of the gap which 
had been left ; it is trying to re- 
move the estrangement which ex- 
isted in the middle of the century.. 



cussions on educational matters confine themselves to the 
ends and means of general or higher instruction;^ in 

We may say that no educational 
scheme can be permanently satis- 
factory that does not regard with 
equal favour, and does not find equal 
room for, the two ideals of Pestal- 
ozzi and Wolf. It is interesting, 
however, to note that neither in 
Switzerland nor in Scotland, the 
two countries in which popular 
education has been longest at 
home, do we find a really great 
development of the higher institu- 
tions and centres of learning ; the 
universities in these two countries 
have always stood somewhat in the 
relation of higher schools to the 
rest of the educational establish- 
ments ; but both countries have 
produced and reared some of the 
greatest geniuses of all time — geni- 
uses who have given to German 
and English literature and science a 
fame over the whole world and for 
all ages ; they would have sufficed, 
had they stayed at home, to form 
academies and universities of the 
first order. 

^ Compare chapter i. pp. 112, 142, 
&c. We are indebted to France 
for three great educational influ- 
ences which have left indelible traces 
over the whole domain of European 
thought. These proceed from the 
Paris University, the model of higher 
education ; the great school of Port 
Royal, that model of secondary 
education ; and the ' Emile ' of 
Rousseau, which gave to the edu- 
cational aspirations of Basedow, of 
Kant, and of Pestalozzi a definite 
direction. It has, however, fre- 
quently been stated that the val- 
uable side of Rousseau's ideas 
was developed outside of France. 
" C'est une chose remarquable," 
says M. Compayrd, " que I'influence 
du philosophe de Geneve se soit 
Burtout exerc^e k I'^tranger, en 
AUemagne et en Suisse" ('His- 

to^re critique des Doctrines de 
I'Education en France,' 5™« ed., 
1885, vol. ii. p. 101). "II y avait, 
chez Rousseau," says M. Br^l, 
" un cote g^n^reux et vivifiant : 
I'amour de I'humanit^.et particu- 
li^rement de I'enfant, la confiance 
dans ses facult^s et le respect de son 
activity intellectuelle. Cette partie 
\\ qui ^tait le germe de vie deposd 
dans les oeuvres de Rousseau, nous 
I'avons laiss^e aux Strangers." In 
French writers a great deal of dis- 
cussion is to be found on the differ- 
ence between education and in- 
struction. Duclos (1704-72) in his 
celebrated 'Considerations sur les 
moeurs de ce sifecle ' (1751), in 
the second chapter, which treats of 
Education and Prejudice, says : " On 
trouve parmi nous beaucoup d'in- 
struction et peu d'^ducation. On 
y forme des savants, des artistes 
de toute esp^ce ; chaque partie des 
lettres, des sciences et des arts y 
est cultivde avec succ^s, par des 
m^thodes plus ou moins conven- 
ables. Mais on ne s'est pas encore 
avis^ de former des hommes, c'est- 
b, dire, de les elever respectivement 
les uns pour les autres, de faire- 
porter sur une base d'education 
gdn^rale toutes les instructions par- 
ticuli6res,"&c. When the successive 
Governments of the Revolution took 
up the question of a national edu- 
cation, the formula of Condorcet 
quite inevitably became more and 
more the leading principle. Con- 
dorcet distinguished "instruction" 
— i.e.y knowledge positive and cer- 
tain, truths of fact and calculation 
— from "education" — i.e., "politi- 
cal and religious beliefs." He gives 
the State the power to extend the 
former, whilst he denies it the right 
to direct and dispense the latter (see 
Hippeau, * L'Instruction publique 
en France pendant la Revolution,*" 



Germany, education and higher instruction present in- 
dependent developments; in England alone the genius 
and language of the nation have refused to admit of any 
curtailment of the original sense of the word. This con- 
tinued to imply a discipline of the character as well as 
of the mind, practical as well as intellectual training. 
So much has been said in this country and abroad re- 
garding the shortcomings of the English universities and 
higher schools, that I feel it a duty to point to the posi- 
tive gain which this ideal of a liberal education^ has 

1881, vol. i. p. xvii ; also Compayre, 
loc. cit., vol. ii. p. 280, &c.) Every 
Government which has attempted 
to systematise, to centralise educa- 
tion, has been forced also to secu- 
larise it, to reduce it to instruction, 
leaving out what many consider the 
central problem of education, the 
training of the character and the 
discipline of the feelings and the 
heart. Considering the large organ- 
isations which have been developed 
in England by the unaided efforts 
of working men, such as the trade- 
unions and the co-operative societies, 
and looking at the amount of self- 
government, self-control, and self- 
denial which they demand from 
their members, one might be tempt- 
ed to say that England is the best 
educated, though it may be the 
worst taught and the least informed, 
of the three nations now under 

1 The term "liberal education 
has acquired a peculiar significance 
in the history of English culture 
and thought. It cannot be trans- 
lated into French or German with 
any certainty that the real signifi- 
cance of the term or the subject 
which it denotes is conveyed. It is 
interesting to note how each of the 
three nations has given to special 
words of the once common Latin 

language a peculiar pregnancy, de- 
noting a peculiar form of thought 
or culture which they have especi- 
ally elaborated. Thus ** science" 
in the modern sense is a product of 
French thought, Wissenschaft a pro- 
duct of German thought. England 
has reserved to itself the elabora- 
tion of a " liberal education." I am 
at a loss how to translate it into 
French, unless I am permitted to 
use simply the word education in 
its contrast to instruction and en- 
seignement, not as this was defined 
by Condorcet, but as it is under- 
stood in the writings of modem 
French educationalists, such as 
Grdard, Brdal, Compayre, and 
others. To convey the meaning 
of ''liberal education" to a Ger- 
man, I would revert to the Greek 
phrase, the iKevdfpios irai^eia of the 
post - classical age. The fact is 
that down to the middle of the 
century the Germans in discussions 
on the work of universities and 
high schools always talk of Wissen- 
scJiaft, English writers always talk of 
" liberal education." To a German 
scholar's heart Wissenschaft is dear 
beyond anything ; to an English 
university man it is "liberal edu- 
cation." The former will sacrifice 
everything to Wissenschaft; the 
latter will not part with "liberal 



been. For it is the principal object of this work to 
attempt to portray the actual progress of thought, the 
valuable contributions of each of the three nations to the 

education." In Germany, the real 
home of the educationalist or Er- 
zieher has not been the university ; 
the home of the man of science has 
not been and is not the university 
in England. The German educa- 
tionalist can point to a special crea- 
tion of his own, the Volksschule. 
The English man of science has 
no organisation to point to except 
it be the select society of a dozen 
great names of world-wide fame, 
corresponding to the solitary and 
unconnected heights of Homer, So- 
phocles, Dante, Shakespeare, and 
Goethe in literature. To descend, 
however, from generalities to the 
real thing, I give here some ex- 
tracts referring to English univer- 
sity life, chosen from among hun- 
dreds, all variations on the same 
theme. Dr Thomas Young, who 
knew both German and English 
universities, having studied at Got- 
tingen and taken his degree at 
Cambridge, was not indebted to 
any university for his position or 
his knowledge ; yet he significantly 
defends the English universities 
against the criticism of the Edin- 
burgh Reviewer : " We do not in- 
tend to imply a censure of the 
system adopted by our universities ; 
. . . for it must be remembered 
that the advancement of learning is 
by no means the principal object of 
an academical institution : the diffu- 
sion of a respectable share of in- 
struction in literature and in the 
sciences among those classes which 
hold the highest situations and have 
the most extensive influence in the 
.State is an object of more import- 
ance to the public than the dis- 
covery of new truths. . . . We 
think that we have observed num- 
erous instances, both in public life 

and in the pursuit of natural know- 
ledge, in which great scholars and 
great mathematicians have reasoned 
less soundly, although more ingeni- 
ously, than others, who, being some- 
what more completely in the pos- 
session of common -sense, . . . were 
still far inferior to them in the re- 
finements of learning or of science " 
('Quarterly Review,' May 1810, 
reprinted in Miscellaneous Works, 
vol. i. p. 235, &c.) I shall now 
give a quotation from an entirely 
different source, from one who in 
his department was equally well 
acquainted with German and Eng- 
lish thought and life. In 1830 E. 
B. Pusey attempted to give his 
friend. Prof. Tholuck of Halle, a 
sketch of what had been " recently 
done in English theology." He 
begins by referring to the "prac- 
tical character of the nation " and 
*' the different condition of the uni- 
versities," and then continues as 
follows : " Few, if any, of our writ- 
ings have originated in an abstract 
love of investigation : our greatest 
and some immortal works have 
arisen in some exigencies of the 
times. ... A German writes be- 
cause he has something to say ; an 
Englishman only because it is, or 
he thinks it is, needed" ('Life of 
Pusey,' vol. i. p. 238). The man 
who did most for the widening of 
the circle of university studies in 
England during the first half of the 
century was William Whewell (1794- 
1866), whose influence at Cambridge 
extended over more than a genera- 
tion. In the beginning he assisted 
the movement begun by Babbage, 
Herschel, and Peacock, and pub- 
lished several text -books on me- 
chanics and dynamics, in which the 
influence of Continental, especially 








tions in 

general stock of ideal possessions, not merely to criticise 
the shortcomings and failures of separate schools of 
thought, or separate sources of mental development. 
Only in the aggregate of these different ideals is to be 
found the inventory of the intellectual possessions, the 
outcome of the higher work of the century. 

When the modern scientific methods and their impel- 
ling force, the mathematical spirit, made their way from 
France to Germany during the first quarter of the century, 

French models, can be clearly traced. 
Between 1830 and 1850 his influence 
exerted itself in two directions, 
firstly by the publication of his 
* History of the Inductive Sciences ' 
(3 vols. 1837 ; a second edition ap- 
peared in 1847, a third in 1857), and, 
secondly, by a series of papers and 
pamphlets referring to university 
education. As the ideal and defini- 
tion of this Whewell adopts the term 
"liberal education." The first of 
these papers appeared in the ' British 
Critic' (No. 17, 1831, "Science of 
the English Universities"). Then 
followed in 1836 " Thoughts on the 
study of Mathematics " ; " Addi- 
tional Thoughts," 1836; "On the 
Principles of English University 
Education," 1837; '*0f a Liberal 
Education in General" (Part 1, 
1845 ; Part 2, 1850 ; Part 3, 1852). 
The second part of the little work on 
Liberal Education gives a history 
of the various changes previous to 
1850 through which the University 
of Cambridge tried to meet the 
growing demands of the times for 
a wider and more liberal programme 
of higher scientific work. In these 
various writings the work of educa- 
tion and " original research" (a term 
introduced by Whewell — see Tod- 
hunter, ' Life of Dr Whewell,* vol. i. 
p. 50), the nature of " permanent" 
and "progressive" studies at the 
university, of "university" and 

" college " education, of " tutorial " 
and " professorial " teaching, are fully 
discussed. In the course of thirty 
years the university of Cambridge 
added to the examinations for ma- 
thematical honours the " Classical " 
Tripos (1822), the " Moral Sciences " 
Tripos and the " Natural Sciences " 
Tripos (1848); also a "Board of 
Mathematical Studies " (1848). Dr 
WTiewell's great influence declined 
when in 1850 Royal Commissions 
were appointed to "inquire into 
the state, discipline, studies, and 
revenues of the universities of Ox- 
ford and Cambridge." He "regarded 
the Commission as an unwarranted 
and undesirable intrusion into the 
affairs of the university." The 
results of this inquiry belong to 
the second half of the 'century. 
Although this movement, which 
was brought about by many in- 
fluences, has somewhat changed the 
issues, the central idea which in 
England tries to assimilate the 
higher work and thought of the 
nation is that of education. The 
term liberal education, which for 
twenty years, from 1830 to 1850, 
formed the banner of university 
reform, has since somewhat yielded 
to "scientific," and more recently 
to " technical," education ; the in- 
fluence of the universities has gone 
out in the work of university exten- 
sion in the provincial towns ; still 


they there met with a powerful intellectual organisation, 
the German university system, in which classical and philo- 
sophical studies had elaborated the ideal of Wissenschaft 
— of science in the larger sense of the word. Gradually, 
and not without opposition, the exact or mathematical 
spirit was received into this system, and has since become 
an integral portion of it. In England the older traditions 
which clung to the two great universities, and the higher 

the whole movement can be de- 
fined as an educational movement. 
Whereas in Germany about a gen- 
eration earlier the term Wissenschaft 
gained the upper hand and governed 
the intellectual life of the nation, 
purely educational movements being 
separated from it, in England the 
purely scientific interest has never 
gained the upper hand, and can 
still complain of having nowhere a 
full and complete representation. 
Around the writings of Whewell as 
a centre may be grouped those of 
A. Sedgwick (* A Discourse on the 
Studies of the University of Cam- 
bridge,' 1833, 5th ed., 1850) ; Sir 
Wm. Hamilton (articles in the 

* Edinburgh Review,' reprinted in 

* Discussions on Philosophy, &c.,' 
1853) ; Sir John Herschel ('A Pre- 
liminary Discourse on the Study 
of Natural Philosophy,' 1831) ; 
the criticisms of Lyell ('Travels 
in North America,' 1845), and of 
the 'Edinburgh,' 'British Quar- 
terly, ' and * Westminster ' Reviews 
('Edin. Rev.,' Ap. 1849, Jan. 1874, 
'Brit. Quart.,' Nov. 1850, 'West. 
Rev.,' Jan. 1855). Whoever desires 
to gain an insight into the different, 
frequently diametrically opposite, 
considerations which moulded and 
governed the reconstruction of the 
German university system on the 
one side, and on the other side 
widened in England the older ideas 
of university education, should com- 

pare the documents relating to the 
foundation of the University at 
Berlin in the beginning of this cen- 
tury (collected by Rudolf Kopke, 
' Die Griindung der Koniglichen 
Fried rich- Wilhelms-Universitat zu 
Berlin,' Berlin, 1860) with the writ- 
ings referred to in this note, and 
centering in Whewell's pamphlets 
and essays. The personification of 
the German scheme was Wilhelm 
von Humboldt, of whom Bockh 
said in his ' Logos epitaphios ' : " He 
was a veritable statesman, pene- 
trated and led by ideas — a states- 
man of a Periclean greatness of 
spirit. Philosophy and poetry, elo- 
quence, historical, philological, lin- 
guistic erudition, were fused in 
him into undisturbed harmony and 
wonderful symmetry." The re- 
forming and revolutionary ideas of 
Fichte, the classical ideals of Wolf, 
the historical interests of J. Miiller 
the historian, the literary interests of 
Schlegel, the philosophical interests 
of Schleiermacher, were combined by 
Humboldt into a realisable scheme. 
Stein said of him in 1810 : " Prussia 
has intrusted the management of 
her educational and scientific in- 
stitutions to a man possessed of a 
remarkable intellect and of great 
firmness of character, and who 
utilises these qualities in his sphere 
of action with glorious loyalty" 
(ibid., pp. 61, 62). 





practical interests of a select class which upheld those 
traditions, prevented any of the Continental ideals, be 
it the philological of F. A. Wolf, or the philosophical of 
Fichte, or the scientific of Laplace and Cuvier, from 
establishing themselves in the older seats of learning. 
And they were, after all, the only organisations for higher 
culture which possessed a historical character and con- 
tinuity. Around these centres, partly in a friendly, more 
frequently in a hostile spirit, other institutions, other 
centres of culture and learning, had grown up. Let us 
rapidly survey these more recent institutions. It is 
hardly necessary again to mention the Koyal Society, 
which was an early offspring of the older universities, a 
kind of overflow of the scientific interests from them into 
31. the capital. More recent was the Eoyal Institution, the 

The Royal - a i 

Institution, creatiou of that extraordinary man, Benjamin Thompson, 
Count Eumford. Like the Eoyal Society, it was de- 
pendent upon private subscriptions and on the popular 
interest created by its lectures. These were very pro- 
miscuous, exhibiting no plan or unity. In the early 
years Dr Young and Davy lectured there, as well as 
Coleridge and Sydney Smith. Later it became the home 
of Faraday, and through him, and many other illustrious 
lecturers, has done much to spread a taste for natural, 
especially experimental, science, in the higher and cul- 
tivated classes. It has been a means of diffusing the 
scientific taste, more perhaps than the exact scientific 
spirit, in the stricter sense of the word. Whilst its 
lectures may have kindled in many a young listener the 
love of scientific work, the Institution did not fulfil the 
early intention of its founder, nor did its laboratory play 




the part of some of the great laboratories of Paris or of 
Germany, in turning out a large number of well-trained 
experimentalists. Davy may be said to have educated 
Faraday, though he was suspected of having become 
jealous of him, and Faraday declared he received only 
one valuable suggestion from any member of his audience 
during the whole course of his lecturing. It is the 
strongly marked individuality of all these great men, 
expressed in their persons, their lives, and their works, 
rather than the character of the institution itself, which 
has given celebrity and historical importance to the Eoyal 
Institution. John Dalton*s ^ position in the Literary and 
Philosophical Society of Manchester was similar to that pjl^^j^j?^ 
of Davy and Faraday in the Eoyal Institution ; and as ^^^ society. 
Faraday can in some sense be called a pupil of Davy, so 
can Prescott Joule ^ be termed a pupil of Daltou, whom 







^ See note, p. 245. 

2 James Prescott Joule (1818- 
89), a native of Salford, "received 
from Dalton his first inducement 
to undertake the work of an ori- 
ginal scientific investigator." He 
was one of the first who tried to 
measure electrical action in terms of 
the units of well-known mechanical 
or chemical changes. His publica- 
tions began in 1840. Weber's ' Elec- 
trodynamische Maasbestimmungen,' 
that great monument of exact meas- 
urement, was published in 1846. 
Mayer's first publication, contain- 
ing a calculation of the mechanical 
equivalent of heat, bears the date 
1842. But the gi-eat publication of 
Gauss, in which he measures mag- 
netic action in ordinary mechanical 
(or absolute) units, dates from 1832 : 
* Intensitas vis magneticae terrestris 
ad mensuram absolutam revocata' 
(Comm. Societ., Getting., 1832, &c.) 

Joule in 1843 published the first 
of his accurate determinations of 
what is termed in physical science 
" J " or " Joule's equivalent of 
heat." He read successively papers 
on this subject before the meetings 
of the British Association, first at 
Cork (1843), giving the constant 
" J " as 838, then as 770, then as 890 
in 1845 (Brit. Assoc, at Cambridge), 
lastly at Oxford (1847) as 781-5. 
From this meeting dates the ac- 
quaintance and scientific co-opera- 
tion of Joule and Thomson (Lord 
Kelvin) and the gradual recognition 
of the importance of the subject 
by other men of science (see Thom- 
son's address on Joule, 1893, in 
• Popular Lectures and Addresses,' 
vol. ii. p. 558 sqq.) Helmholtz's 
memoir, " Ueber die Erhaltung der 
Kraft," which was theoretical — as 
Joule's w^ere experimental — dates 
also from 1847. 

Hi, " py ffW| ig «i »«aiffai-p-iw 

" trnt t liianjL-MiiPi i ^iiwif 





he succeeded as president of the Society. These names 
are identified with some of the greatest work in experi- 
mental science. Some of them may be said to be iden- 
tified with quite original theoretical ideas which have 
governed the development of great departments of re- 
search ever since. Dalton's atomic theory in chemistry, 
however, received a tardy recognition in England, and 
was firmly established only by foreign research, while 
Faraday's " lines of force " remained a mystery to elec- 
tricians,^ till William Thomson and Clerk Maxwell made 
them the groundwork of our most recent conceptions. 
It is well to note that neither Young, nor Davy, nor 
Faraday, nor Dalton, nor Joule belonged to the circle 
of Cambridge men, and that probably none of them re- 
ceived any inspiration from that official school of English 
mathematics.^ In the early years of the century that 

1 See Helmholtz on Faraday's 
ideas in ' Vortnige und Reden,' vol. 
ii. p. 277. '* Since the mathemati- 
cal interpretation of Faraday's theo- 
rems has been given by Clerk Max- 
well in methodically elaborated 
scientific formulse, we see, indeed, 
how much definiteness of conception 
and accurate thought were con- 
tained in Faraday's words, which 
seemed to his contemporaries so 
indefinite and obscure. And it is 
indeed remarkable in the highest 
degree to observe how, by a kind 
of intuition, without using a single 
formula, he found out a number of 
comprehensive theorems, which can 
only be strictly proved by the 
highest powers of mathematical 
analysis. I would not depreciate 
Faraday's contemporaries because 
they did not recognise this ; I 
know how often I found myself 
despairingly staring at his descrip- 
tions of lines of force, their number 

and tension, or looking for the 
meaning of sentences in which the 
galvanic current is defined as an 
axis of force, and similar things. 
A single remarkable discovery can 
indeed be brought about by a happy 
chance, . . . but it would be against 
all rules of probability that a numer- 
ous series of the most important 
discoveries, such as Faraday pro- 
duced, could have had their origin 
in conceptions which did not really 
contain a correct, though perhaps 
deeply hidden, ground of truth." 
2 Young resided at Cambridge to 
take his medical degree on his re- 
turn from Gottingen ; but though 
his biographer has inserted a chap- 
ter on Cambridge in the ' Life of 
Young,' and though Young's first 
great discovery, that of the inter- 
ferences of waves of sound and light, 
fell within that period, there is no 
evidence that his scientific studies 
were promoted by Cambridge influ- 

centre had, indeed, to receive aid from a still more 
secluded and unacademic quarter. Undergraduates of 
Cambridge used to migrate from the seat of teaching 
which has been immortalised by Newton to the remote 
Yorkshire village of Sedbergh, where John Dawson,^ one 33. 

^ John Daw- 

of the few British analysts who held their own agamst s^^f^ ^ 
the great foreign authorities, taught the higher mathe- 
matics for five shillings a-week. 

During the latter part of the eighteenth century a 
formidable rival to the learning of Oxford and Cambridge 
had sprung up in the Scotch universities. These were 34. 

. The Scotch 

teaching centres, more after the manner of the loreign univer- 

o ' sities. 

universities. They had been started on the model of the 
University of Paris or of the older Italian universities ; 
some had their origin in the educational movement which, 
especially in those countries where the doctrines of Calvin 
prevailed, accompanied the Keformation.^ All through the 

ences ; in fact he makes a disparaging 
remark regardingBritish as compared 
with Continental mathematics. See 
Peacock's 'Life of Dr Young,' p. 127. 
1 John Dawson (1734-1820), the 
son of a poor " statesman" of Gars- 
dale, tended his father's sheep till 
he was twenty. He studied mathe- 
matics with innate love and ability, 
inventing a system of conic sec- 
tions out of his own brain. By 
teaching he gained a little money. 
In 1756 he instructed three young 
men — of whom Adam Sedgwick's 
father was one — before they went 
up for their Cambridge studies. He 
then became assistant to a surgeon 
at Lancaster. Having saved £100 
he walked to Edinburgh and studied 
medicine there. His funds spent, 
he returned to Sedbergh, where he 
practised as a surgeon. WTien he 
had saved a larger sum he proceeded 

with this to London. After tak- 
ing his degree in 1767, he settled 
in his native county to practise his 
profession and teach the higher 
mathematics to Cambridge under- 
graduates. They flocked to him 
in the summer, and between 1781 
and 1794 he numbered eight senior 
wranglers among his pupils. In 
1797 and subsequent years he 
counted four more. In 1812 he 
ceased teaching. He wrote papers 
on the " precession " and the lunar 
theory, and followed the develop- 
ment of higher mathematics on the 
Continent. See 'Life and letters 
of Adam Sedgwick,' by J. W. 
Clark and T. M'K. Hughes, 1890, 
vol. i. p. 61, &c. 

2 Details referring to the founda- 
tion of the Scotch universities are 
given by Sir A. Grant in the first 
volume of his * Story of the Univer- 





seventeenth and eighteenth centuries they stood in inti- 
mate relations with such Continental centres of study as 
Paris, Geneva, and the Dutch universities. Adam Smith 
and David Hume were in direct and very intimate inter- 
course with French thought, the former having obtained in 
France a knowledge of the novel views of the great politi- 
cal economists of the pre-revolutionary period. Edinburgh 
became in the first half of the last century, under the 
influence of John Monro and his son Alexander (1697- 
1767), who was a pupil of Boerhaave, a medical school 
of great importance, rivalling London in its foreign rep- 

sity of Edinburgh,' 2 vols., 1884. 
Three of them— St Andrews, Glas- 
gow, and Aberdeen — were founded 
in the centuiy preceding the Re- 
formation ; St Andrews about 
1411 by Bishop Wardlaw, because 
Scotch students had been un- 
popular and " molested " at Ox- 
ford. The University of Glasgow 
was founded in 1450, reference 
being made to the University of 
Bologna in the Bull of Pope Nicholas 

V. ; but it has also been observed 
that **the customs and technical 
phraseology showed an imitation of 
the institutes of Louvain, then 
and for all the following century 
the model university of Northern 
Europe, of which a Scotchman, 
John Lichton, had been Rector" 
(p. 21). Aberdeen was started by 
Bishop Elphinstone, who had studied 
in Glasgow and Paris, and been pro- 
fessor, both there and at Orleans, of 
canon and civil law. In the pre- 
amble to the Bull of Pope Alexander 

VI. the Universities of Paris and 
Bologna are referred to (p. 29). 
But the universities seem not to 
have flourished previous to the Refor- 
mation, when they were " purged " 
and a new spirit and order infused 
into them. St Andrews was to have 
four faculties, named as in foreign 

universities — Philosophy, Medicine, 
Law, and Divinity (p. 63). Glas- 
gow and Aberdeen were to have 
two faculties, of which the first 
was to be Philosophy (or Arts), 
the second to comprise Law and 
Divinity. The ' Book of Discipline ' 
contained a very complete scheme 
of higher graded education ; but 
this was only gradually and par- 
tially realised ; secondary schools 
being wanting, the " colleges " had 
to descend to elementary teaching 
(p. 67). A jealousy also existed on 
the part of those in power regard- 
ing the older universities, these 
being— as the King of France de- 
clared when refusing to grant to 
the Academy of Geneva the rights 
of a university — hotbeds of heresy 
(p. 125). Accordingly the latest 
academic creation in Scotland was 
the foundation by the **Town 
Council and ministers of the city " 
of the College of Edinburgh (pp. 
99, 121, 127) between the years 
1561 and 1578, King James's char- 
ter dating from 14th April 1582. 
**But it did not, like the older uni- 
versities, commence with a blaze 
of success and then collapse. It 
started from a humble beginning 
and steadily expanded into greater 
things" (p. 158). 

utation.-^ Edinburgh had also one of the earliest chairs 

of chemistry. It grew into an independent centre of 35. 

The Royal 

original scientific work when in 1783 the Eoyal Society society of 

° ^ ,/ J Edinburgh. 

of Edinburgh was incorporated. Ever since the founda- 
tion of the Scotch universities, mathematics had been 
studied independently in Scotland, where John Napier 
of Merchiston had at the end of the sixteenth century 
invented logarithms. " Whether we consider the great 
originality of the idea, the difficulty of carrying it into 
effect in the state in which algebraical analysis then was, 
or the immense practical and theoretical value of the inven- 
tion, we shall have little difficulty in claiming for Napier 
the honour of a discovery unsurpassed in brilliancy in 
the whole history of mathematics." ^ From that time the 

^ " In 1738 the foundation-stone 
of that building which was till re- 
cently the Royal Infirmary of Edin- 
burgh was laid, and a great public 
enthusiasm on the subject was mani- 
fested. Drummond, the greatest 
^dile that has ever governed the 
city of Edinburgh, and Monro, were 
appointed the Building Committee, 
and they paid the workmen with 
their own hands. All classes con- 
tributed : landowners gave stone ; 
merchants gave timber ; farmers 
lent their carts for carriage of 
materials ; even the masons and 
other labourers gave one day's work 
out of the month gratis, as it was a 
building for the benefit of the poor " 
(Sir A. Grant, loc. cit.j vol. i. p. 

2 Quoted by Sir A. Grant {loc. 
cit.f vol. ii. p. 293) from Chryetal's 
unpublished Inaugural Address, 
* John Napier, Baron of Merchiston ' 
(1550-1617). The *Mirifici Logar- 
ithmorum Canonis Descriptio' ap- 
peared in 1614. The 'Logarithmo- 
rum Chilias prima ' of Henry Briggs 

(1556-1630), professor at Oxford, 
contains the first table of com- 
mon or decimal logarithms. 
Kepler (1571-1630) received the 
invention with great enthusiasm as 
of immense importance to astro- 
nomy. "The more one considers 
the condition of science at the time, 
and the state of the country in 
which the discovery took place, 
the more wonderful does the in- 
vention of logarithms appear. . . . 
It is one of the surprises in the 
history of science that logarithms 
were invented as an arithmetical 
improvement years before their 
connection with exponents was 
known. It is to be noticed also 
that the invention was not the re- 
sult of any happy accident. Every- 
thing tends to show that it was 
the result of many years of labour 
and thought undertaken with this 
special object ; Napier succeeded in 
devising, by the help of arithmetic 
and geometry alone, the one great 
simplification of which they were 
susceptible — a simplification to 



The • Edin- 

science was cultivated at the different Scotch universities, 
which supplied Oxford with a Professor of Astronomy 
(preferred to Halley), in the person of David Gregory. 
" David Gregory not only introduced the ' Principia ' to 
Edinburgh students, but he also brought them to the 
notice of Englishmen." ^ The Philosophical (afterwards 
called the Koyal) Society of Edinburgh was much in- 
debted to Colin Maclaurin,^ who almost alone with Landen 
and Ivory maintained the reputation of British mathe- 
maticians during seventy years, whilst the Continental 
school was revolutionising that science. A successor to 
Maclaurin in the mathematical chair at Edinburgh, John 
Playfair,^ introduced the Continental methods into the 
studies of the Scotch universities about the end of the 
last century. He was one of the early contributors to 
the * Edinburgh Keview,' which in politics, literature, 
and science inaugurated a new kind of criticism, and led 
a powerful attack upon all those traditional forms of 
government, taste, and learning which prevented the free 
expansion of ideas and the progress of science and prac- 
tical interests. Though not always judiciously used, the 

which the following two hundred 
and eighty years have added no- 
thing" (Glaisher in 'Ency. Brit.,' 
9th ed., article "Napier"). 

1 David Gregory (1661-1708) has 
"the honour of having been the 
first to give public lectures on the 
Newtonian philosophy. This he did 
in Edinburgh five-and-thirty years 
before these doctrines were accepted 
as part of the public instruction in 
the university of their inventor" 
(Sir A. Grant and Chrystal, loc. 
cit., vol. ii. p. 296). Cambridge 
writers, headed by WTiewell, are 
loath to admit any reluctance on 

the part of their university in ac- 
cepting the Newtonian philosophy, 
in spite of Whiston's testimony to 
the contrary. See on this Whewell's 
• History of the Inductive Sciences,' 
3rd ed., vol. ii. p. 149, &c. 

2 Colin Maclaurin (1698-1746) 
published, 1742, a 'Treatise on 
Fluxions,' 2 vols. 4 to. In 1740 he 
shared with Daniel Bernoulli and 
Euler the prize of the French Aca- 
demy for his ' Essay on the Tides.' 

3 John Playfair (1748-1819) was 
Professor of Mathematics and then 
(from 1805) of Natural Philosophy. 



influence of that review must have been very powerful 
in rousing the older English universities out of a state 
of stagnation, and especially in stimulating younger minds 
in the direction of the long-delayed reform of studies. 
An important step in this direction was taken by three 87. 

The Analy* 

undergraduates of Cambridge — Herschel, Babbage, and ticai society 
Peacock — who in 1812 formed the Analytical Society, ^^^s^- 
with the distinct object of introducing the more modern 
and powerful analytical methods developed mainly by 
Euler and Lagrange, and deposited in their numerous 
Memoirs in the publications of the foreign academies.^ 
In harmony with them worked Whewell, Airy, and 
Sedgwick, who did much to enlarge the programme of 
mathematical and scientific studies, though they very 
staunchly upheld that the real object of university 
education could not be identified with any special 
method or school of thought, but was expressed in 
the specific ideal peculiar to England, that of a liberal 

The universities of Scotland, unlike those of England, 
instead of nursing an exclusive spirit, and encouraging wein 

^ r > & & Scotland. 

only scanty intercourse between teachers and students of 
different centres, lived in constant exchange of professors 
and ideas — much in the same way as has always been the 
custom on a larger scale among German and other Conti- 
nental universities. Though this is destructive of that 
individual character of the university or the college which 


^ See note 1 to p. 233 ; also for 
many details Rouse Ball's ' History 
of the Study of Mathematics at 
Cambridge,' 1889, p. 120, &c. 

2 On Whewell and his writings 
on university education see note 

to p. 261. Sir George Biddell 
Airy (1801-1891) published in 1826 
* Mathematical Tracts* (2nd ed., 
1831) on the lunar and planetary 
theories, &c., for the use of students 
in the university. 



is so highly prized by many English fellows, it is certainly 
more conducive to the progress of studies and of research, 
and it is the cause why in the early history of recent 
science the universities of Scotland have played so much 
more important a part than those of England. Whilst in 
England modern science was cultivated outside the pale 
of the universities by Priestley, Davy, Wollaston, Young, 
Dalton, Faraday, and Joule, to whom we may even add 
Green and Boole, all eminent Scotch men of science, such 
as Gregory, Simson, Maclaurin, Playfair, Black, Thomson, 
Leslie, Brewster, and Forbes, were university professors, 
many of whom did not confine their labours to one centre, 
but spread the light of their ideas and researches all over 
the country.^ Whilst England has been great in single 
names, Scotland has certainly in proportion done more 

1 Napier of Merchiston remained 
outside the pale of the universities. 
At that time the College of Edin- 
"burgh had no mathematical pro- 
fessor ; but Glasgow had, and so 
had Aberdeen. James Gregory was 
educated at Aberdeen, was then pro- 
fessor at St Andrews, and subse- 
quently at Edinburgh. Colin Mac- 
laurin was educated at Glasgow, 
then professor at Aberdeen and at 
Edinburgh. Playfair was educated 
at St Andrews, and lectured there 
before coming to Edinburgh. Leslie 
was trained at St Andrews, and was 
then professor first of mathematics 
and afterwards of natural philosophy 
at Edinburgh. Black was educated 
at Glasgow and Edinburgh, and 
was professor at both universities. 
Brewster studied at Edinburgh, and 
was subsequently principal of St 
Andrews and then of Edinburgh. 
Forbes, as student and professor, be- 
longs exclusively to Edinburgh, and 
80 did in earlier times Robert Sim- 

son, the great mathematical pro- 
fessor. Adam Smith belongs exclu- 
sively to Glasgow, though he had 
lectured in Edinburgh before he 
was appointed professor at Glasgow. 
But the contrast between England 
and Scotland becomes still more 
prominent if we look at the medi- 
cal sciences and note the great 
array of celebrated professors at 
Edinburgh, CuUeu, Brown, Gregory, 
Alison, Hamilton, Syme, Simpson, 
Christison, and Charles Bell, where- 
as the equally great names of John 
and William Hunter, of Jenner, of 
Astley Cooper and Bright, have no 
connection with the English univer- 
sities ; Sydenham was only slightly 
connected with Oxford and Cam- 
bridge, and even Harvey never 
occupied a prominent position at 
Oxford. Through situation or con- 
stitution the English universities 
were unable to open a field of ac- 
tivity for these celebrated men. 


to diffuse modern scientific knowledge. The great pub- 
lishing firms of Edinburgh have also for more than a 
century done much through Cyclopaedias, Eeviews, and 
Magazines to spread general information of all kinds ;^ 
whilst Hume, Adam Smith, and the subsequent Scotch 
school of metaphysicians have exerted their influence 
during the whole of this century, not only in Great 
Britain, but over the whole of Europe.^ In the more 
circumscribed domain of scientific thought a powerful 
influence has again been exerted from Scotland as a 
centre, and through the larger instrumentality of the 
University of Cambridge, on the study of mathematical 
and experimental physics, and what we may term the 
spirit and method of these sciences. This influence be- 

^ The most popular Cyclopaedia, 
that of Chambers, had its origin in 
Edinburgh in 1860. It was founded 
on the tenth edition of Brockhaus's 
' Conversations-Lexicon.' The more 
important 'Encyclopaedia Britan- 
nica' was published there also in 
1771, 3 vols. ; 2nd ed., 1777. The 
* Edinburgh Review ' was estab- 
lished in 1802 by Jeffrey, Scott, 
Horner, Brougham, and Sydney 
Smith ; it was the first successful 
"Quarterly," carried on independ- 
ently of the booksellers, after 
several unsuccessful attempts had 
been made in a similar direction by 
Adam Smith and Hugh Blair in 
1755, and after Gilbert Stuart and 
William Smellie had issued from 
1773 to 1775 the 'Edinburgh Mag- 
azine and Review.' No such peri- 
odical ever attained to the circula- 
tion of the 'Edinburgh Review,' of 
which at one time 20,000 copies 
were sold. The first high -class 
monthly Magazine was also printed 
in Edinburgh by. Blackwood in 
1817, with Scott, Lockhart, Hogg, 


Maginn, Syme, and John Wilson as 
contributors. 'Tait's Edinburgh 
Magazine' was the first shilling 
magazine. The brothers William 
and Robert Chambers, in 1832, 
started the Journal named after 
them. They also brought out many 
popular works of sterling merit, 
mostly written by Robert Cham- 
bers, than whom none did more to 
introduce a knowledge of nature 
into popular reading, and to give a 
healthy tone and moral influence 
to the cheap literature which has 
become such an important factor 
in modern culture. 

^ Whilst Locke exercised the 
greatest influence on French phil- 
osophy, Kant starts more directly 
from Hume. The literature of the 
Restoration in France again at- 
taches itself to the Scotch meta- 
physicians, notably Reid. It is 
interesting that both Kant and 
the greatest representative of the 
French " Ideology," De Tracy, were 
of Scotch descent. 







longs to the second half of the century, and is centred in 
the two names of William Thomson (Lord Kelvin) and 
James Clerk Maxwell, who may be said to have jointly 
revolutionised natural philosophy. It began with the ap- 
pearance of George Stokes's and William Thomson s im- 
portant contributions to mathematical physics, and with 
the publication of that suggestive and stimulating — but 
unfortunately unfinished — work by Thomson and Tait on 
Natural Philosophy. It was represented to the fullest 
extent in Clerk Maxwell's activity in the Cavendish 
Laboratory at Cambridge. But the consideration of this 
subject belongs to a later chapter of the present work, 
and is only mentioned here in connection with the intel- 
lectual intercourse and exchange which has existed all 
through this century between the invigorating spirit of the 
north and the more conservative spirit of the southern 
39. portion of the island. Besides Scotland another centre 
MSJfmlil —the Dublin School— has gained European renown 
cai school, ^j^^^^g^ ^ Qf mathematical labours of the highest 

importance, some of them of an originality hardly yet 
sufficiently recognised. This school is represented by 
the names of Kowan Hamilton,^ MacCuUagh, Sal- 


1 Of Rowan Hamilton's dynami- 
cal "principle of varying action" 
I have spoken in a note to p. 231. 
William Rowan Hamilton (1805-65) 
cannot with the same certainty as 
Kant and De Tracy be claimed as 
of Scotch descent. Indeed he 
seems to belong distinctly to Ire- 
land. See Tait's article in the 
' North British Review,' September 
1866, and Perceval Graves's reply in 
'Life of W. R. Hamilton' (3 vols., 
1882-89, vol. i. p. 5). He was one 
of the few quite original mathe- 

maticians who, like Gauss, led the 
way into new channels of thought 
and succeeded in breaking through 
the traditional forms of this science, 
which more than any other is ham- 
pered in its development by trans- 
mitted customs and habits of repre- 
sentation. Thus, after ten years of 
research and thought in connection 
with the representation of extend- 
ed algebraical forms by means of 
the different directions in space, he 
succeeded in establishing the fun- 
damental principle of his theory of 


mon ; ^ nor should we forget the suggestive writings of 
George Boole.^ The influence of these men originated 
outside of Cambridge, and a history of mathematics at 
that university does not contain their names,'^ though the 
ideas of which they have been the bearers have largely 
entered into the text-books and the teaching of the Cam- 
bridge school. 

So far I have mainly dealt with one side only on which 
the progress of science depends, namely, the methodical 
use of experiment, measurement, and calculation; this 

quaternions — complex quantities 
which are compounded of a purely 
algebraical or quantitative element 
and three distinct elements corre- 
sponding to the three directions or 
dimensions of space. He was the 
first to work out this calculus, and 
the labour occupied twenty years 
of his life. In Hamilton's calculus 
of quaternions, distance (or length) 
and direction are introduced as they 
naturally present themselves when 
we deal with geometrical or physical 
problems, instead of all quantities 
being reduced to lengths, as was 
the case in the Cartesian geometry. 
Hamilton thus broke through the 
conventionalism of the latter and 
showed how the consideration of di- 
rections in space forces us to extend 
the original operations of arithmetic. 
It is 'interesting to note how simul- 
taneously Grassmann (see p. 243, 
note 1 ) in his ' Ausdehnungslehre ' 
(1844) and Von Staudt in his 'Geo- 
metric der L4ge' (1847), quite inde- 
pendently worked at similar exten- 
sions of our arithmetical and geo- 
metrical conceptions, and how sub- 
sequently quaternions, in which 
Hamilton had seen a powerful me- 
thod for solving geometrical and 
physical problems, present them- 
selves as a special form of the ex- 
tended algebra and geometry elabor- 

ated from these diflFerent beginnings. 
Whilst the practical usefulness of 
the calculus has been demonstrated 
by some extensive applications, as, 
for example, to spherical trigono- 
metry, the ideas contained in it^ — 
frequently without Hamilton's no- 
tation—are gradually finding their 
way into text- books, and the strange- 
ness which for half a century pre- 
vented the labours of Hamilton, 
Grassmann, and Von Staudt from 
being generally appreciated, is dis- 
appearing. A popular exposition 
of the relation of quaternions to 
general arithmetic is given in 0. 
Stolz, 'Grossen und Zahlen,' Leip- 
zig, Teubner, 1891. 

^ The excellent treatises of Sal- 
mon on * Higher Algebra,' 'Higher 
Plane Curves,' 'Geometry of Three 
Dimensions,' and ' Conic Sections ' 
have in their German translations 
by Fiedler done a great work in 
systematising and popularising mo- 
dem conceptions in algebra and 
geometry. See Gino Loria's treatise 
on the " Principle Theories of Geo- 
metry " in the German translation 
by Schutte, Leipzig, 1888, p. 25, 

2 See p. 247, note 2. 

3 See Rouse Ball, ' A History of 
the Study of Mathematics at Cam- 
bridge,' 1889. 







of British 
tions to 

Diffusion of 
on the 

side had been very largely developed by the great French 
naturalists and mathematicians in the beginning of our 
period. The change in the higher branches of science 
which took place during the first half of the century is 
greatly owing to them, and to the later German school, 
which was much influenced by them. If we compare 
the contributions of British science in these branches, 
they are indeed inferior in bulk, and still more so in 
methodical arrangement; but among them is a small 
number of works of the first order which are embodi- ' 
ments of scientific ideas of the very highest importance. 
Introduced into the great edifice of scientific research 
which was being planned and erected on the Continent, 
they mark the very corner-stones of the building, stand- 
ing out in bold and conspicuous prominence. But it is 
a fact that no Academy existed in this country which 
was zealous in collecting and arranging all the best 
labours of scattered philosophers, no university which 
was anxious to attract and train promising intellects, 
no comprehensive text-books and hand-books, ensuring 
right guidance, correctness of knowledge, and complete- 
ness of study, no historical and philosophical traditions 
guaranteeing that novel contributions should make their 
appearance under favourable conditions, or supplying the 
most appropriate 77iise en sdne for new ideas. 

It is the French Institute, in the earlier years of the 
century, and the German university system, with its 
many local ramifications and literary organs, during the 
whole of the century, which have done the great work 
of systematising and diffusing scientific knowledge, and 
of introducing the exact spirit of research. There is 



something casual and accidental about the great ideas 
which British men of science contributed during the first 
half of the century. Each of them chooses an isolated 42. 

Isolation of 

position, a special form of delivery, frequently a Ian- Englishmen 

•*^ ' ^ J » T. J of science. 

guage and style of his own. They attach little or no 
importance to the labours of others, with which they 
are frequently unacquainted.^ Important papers are 
lost or buried, as in the case of Cavendish and Green. 
Novel ideas are communicated in unintelligible language 
and symbols, and accordingly neglected. This was the 
case with Dr Young's writings, and to a certain extent 
with Faraday's. The greatest discoveries were unduly 
postponed through the absence of assistance, as, seems to 
have been the case with Adams's discovery of Neptune,^ 
perhaps with Stokes's anticipation of spectrum analysis.^ 

^ This is correct of most of the 
great men referred to in the course 
of this chapter. Among them, how- 
ever, Rowan Hamilton forms an ex- 
ception. Though working on quite 
original lines, he took a great in- 
terest in the labours and sugges- 
tions contained in the writings of 
his forerunners and contemporaries, 
as the historical notices in the pre- 
face to his 'Lectures on Quater- 
nions' (1853) prove; likewise his 
correspondence with De Morgan (see 
* Life of Sir W. R. H.,' vol. iii.) 

^ The story of the discovery of 
Neptune has been frequently told. 
The first publication of the ele- 
ments of the suspected planet, 
which enabled a search to be made, 
came from Leverrier to the Paris 
Academy of Sciences on the Ist 
July and the 31st August 1846. 
In consequence of this publication, 
Galle at Berlin, requested by Lever- 
rier to search in the neighbourhood 
of 8 Capricomi, and comparing his 
observations made on the same 

night on which he received the 
request, 23rd September 1846, with 
Bremiker's map, actually found the 
planet. Subsequently it became 
known that Adams of Cambridge 
had already communicated his 
elements in September and October 
1845 to Challis and Airy, and that 
the former had actually seen the 
planet on the 4th and 12th of 
August 1846, but — for want of 
equally detailed maps — had not 
compared the observation and estab- 
lished the discovery. See Whe well's 
* History of the Inductive Sciences,' 
third ed., 1857, vol. ii. p» 460, &c. ; 
also Wolf, * Qeschichte der Astro- 
nomie,' p. 537, &c. 

' It appears from a communica- 
tion of Sir William Thcmison (Lord 
Kelvin) to Kirchhoff immediately 
after the latter had published in 
1859 his explanation of the iden- 
tity of the dark lines in the solar 
spectrum with the bright lines in 
the spectra of coloured flames, that 
Stokes, soon after the publicatioa 





What might not these great minds have accomplished had 
they attached the same importance to style and form as 
most of the great French men of science, or had they been 
called upon to teach a number of eager pupils, anxious, 
not to take honours and degrees, but to understand and 
further elaborate the suggestions of their masters, as has 
been the custom and tradition in Germany ? The history 
of English science during the first half of the century 
consists of a series of biographies, or of monographs on 
single ideas and points of view. We are struck by the 
individual greatness of the minds which produced them, 
their originality or the suddenness of their appearance. 
An doge by the permanent secretary of the Academy has 
usually been considered sufficient to satisfy the historian 
of science in France ; the life of every great philosopher 
in Germany is identical with the history of a phase of 
thought or with a school of research ; in England alone 
the person of the thinker has nearly always claimed the 

by Miller in 1845 and by Foucault 
in 1849 of observations relating to 
this subject, had suggested in the 
course of conversation that there is 
a correspondence between emission 
and absorption of the same kind of 
light by the vibrating molecules of 
the same body, according as it is 
used as a source or a screen for 
light Had this idea of Stokes's, 
which suggested the presence of 
sodium in the atmosphere of the 
sun, been followed out at the time, 
the discovery of spectrum analysis 
would have taken place ten years 
earher. Actually, the various pub- 
lications, beginning with Fraun- 
hofer's description of the dark lines 
in the solar spectrum in 1814 and 
proceeding through the observa- 
tions of Herschel, Talbot, Drum- 

mond, Miller, Angstrom, Pliicker, 
Swan, and Balfour Stewart on 
the absorption and radiation of 
heat, found their consummation 
when Bunsen and Kirchhoff settled 
the main point in question — viz.y 
"that the bright lines of an in- 
candescent gaseous body depend on 
the chemical constituents of the 
same." Then at length spectrum 
analysis became possible. See on 
this matter Kirchhoff 's own histori- 
cal risumi of the year 1862, re- 
printed in 'Gesammelte Abhand- 
lungen' (Leipzig, 1882), p. 625, 
&c. ; also Sir William Thomson's 
' Baltimore Lectures,' shorthand 
notes, 1884, p. 100, and Stokes's 
translation of Kirchhoflf's first paper 
in 1860 (• Philos. Magazine,' March 

greater share of popular attention.-^ His mental labours 
have preserved an individual character, shutting them 
out during his life from common contact, and limiting 
their fertilising power, like that of an oasis in the desert, 
to a narrow circle of casual visitors. Minds like Newton 
and Faraday, full of new life, but modestly content with 
deepening and strengthening their secluded vigour, re- 
frained from boastful publicity or ostentatious parade, 
working for all ages rather than for a special school or a 
passing generation. It is the individualism of the English 43. 

^ ^ ^ ° . Individual- 

character, the self-reliant strength of natural genius, which ism of the 

' o o » English 

comes out most strongly in its great examples of scientific character, 
work. In characters of smaller breadth, in intellects of 
lesser power, these tendencies show themselves in ways 
which we cannot always admire or commend : in the 
emulation for place and position, in the competing for 

^ This explains the remarkable 
richness of English literature in, 
biographies, containing copious col- 
lections of correspondence, and the 
almost total absence of such litera- 
ture in France, which, on the other 
side, is rich in memoira, written by 
statesmen and authors themselves. 
As the students of nature have 
usually little time for autobio- 
graphy, we possess of the long list 
of great names in modem French 
science hardly any personal records 
such as are so plentiful in English 
literature. What we miss in many 
of these elaborate and frequently 
gossiping narratives is a just ap- 
preciation of the position of the 
subject of the bic^aphy in the 
history of science, literature, and 
thought, a definition of the exact 
place and importance which belongs 
to him and his work. This is what 
is given in such a masterly and con- 
densed form in the better iloges of 

Fontenelle, of Cuvier, of Arago, 
and other secretaries of the French 
Academies. In Germany biographi- 
cal literature is less developed than 
in this country, and memoirs are 
almost absent — those of Varnhagen 
von Ense and of Perthes, among 
literary men, being remarkable and 
rare exceptions. Similarly the great 
correspondence carried on by Goethe 
through nearly sixty years is a 
unique monument of his genius 
and his influence, comparable only 
to that of Voltaire during the last 
century. R. Haym in his biographies 
of Hegel, Wm. von Humboldt, and 
Herder, which combine the bio- 
graphical with the historical and 
critical elements, has done a great 
work, and these books are invalu- 
able contributions to the history of 
thought. Justi's * Winckelmann ' is 
of equal importance ; but Dilthey's 
* Schleiermacher * is unfortunately 





honours and championships — in all the noble and ignoble 
forms of racing, where much energy, which might more 
usefully have been merged in co-operative action, is 
sacrificed for the sake of individual distinction. But 
where the height of genius forbids emulation, where the 
towering intellect has distanced all records, this indi- 
vidualism has produced single specimens of the greatest 
work, examples of the highest moral worth. It is not in 
the courses of scientific work alone that we shall have 
occasion to mark the peculiarity of British, especially of 
English, thought ; but it is interesting to note how even 
in this sphere, which more than any other seems to bear 
an international and cosmopolitan character, the genius 
of the nation strongly asserts itself, baffling every effort 
to control it or to lead it into more conventional chan- 
44. nels. The last fifty years have done much to destroy 
durSg^he the peculiarly national customs, the idiosyncrasies of the 

last fifty JT t' 

years. different peoples. English institutions have been copied 
in France, and German customs introduced into England ; 
it has recently been stated that the older type of scientific 
amateur which existed in this country is dying out, being 
rendered impossible by the more complicated machinery 
of science, the manifold conditions on which progress de- 
pends. It seems to me doubtful whether this view is 
correct. Surely the advance of the highest kind of 
thought will always depend upon the unfettered devel- 
opment of the individual mind, regardless of established 
habits, of existing forms of expression, or of adopted 
systems ; just as the diffusion and wholesale application of 
single discoveries will depend on a ready and efficient ma- 
chinery and organisation ; whilst their influence on gen- 

eral thought and literature will depend on the cultivation 
of a perfect form, of an expressive and elegant style. The 
French alone in the beginning of the century could boast 
of the last ; the Germans have most successfully developed 
the second ; whilst England, the country of greatest indi- 
vidual freedom, has been the land most favourable to the 
growth of genius as well as eccentricity, and has thus pro- 
duced a disproportionate number of new ideas and depart- 
ures. Nor is it to be desired that the reliance of genius 
on itself should be in any way curtailed, as it is impos- 
sible to foretell whence the new light will come which is 
to illuminate future ages. This individualism of the 
English mind presents other accompanying features, and 
these are of great interest to the historian of thought. 
They manifest themselves in the province of science as 
much as in other provinces. We will now study them 
more closely ; in the sequel we shall meet with them in 
other departments also. 

Hitherto our observations on English science have nearly 
all referred to only one side of modem scientific work, — 
the side on which lie the experimental, measuring, and cal- 
culating sciences ; those sciences which abroad are termed 
" exact " ; in which mathematical notions and methods, 
be it of measurement or of calculation, obtain. But these 
sciences cover only one side of reality. We noticed how in 
France, during the great scientific epoch, the other side of 
nature, that which exhibited and was filled by the pheno- 
mena of life, was simultaneously explored with equal 
originality and equal success. As Laplace was the great 
representative of the one, so Cuvier was the great re- 
presentative of the other. We have also seen how in 





Germany this latter department of research was specially 

cultivated, how all the mathematical, experimental, and 

philosophical sciences combined to organise the one great 

45. science of physiology or biology, with its central and 

British con- . . ^^» 

tributionsto crowning problcm — the problem oi consciousness, we 

biology. ® ^ ^ £ ' 

also noted how this science worked a great reform m 
the whole domain of medical theory and practice. Let 
us now return to the question, What has Great Britain 
done during the first half of this century in this great 
department of scientific thought ? Single great names, like 
those of Harvey,^ marked in former centuries discoveries 
in the natural sciences equal to those of Newton in the 
mathematical ; the name of Eay^ is still preserved in the 

Society called after him : in more recent times Hutton 
formed a school in geology which was opposed to that of 
Werner, emanating from Germany.^ Hunter, the anato- 

1 William Harvey (1578-1657), a 
native of Kent, received his medical 
education in Italy, especially in 
Padua, under Fabricius of Acqua- 
pendente. The discovery of the 
circulation of the blood belongs to 
the year 1616, and is almost con- 
temporary with Napier's invention 
of logarithms. This discovery is con- 
tained in the manuscript of Harvey's 
lectures preserved in the British 
Museum, but the publication did not 
take place till 1628 ( ' Exercitatio 
anatomica de motu corporis et san- 
guinis in animalibus,' published at 
Frankfort). Although Harvey was 
drawn into long controversies by 
his publication of this work, he 
had the satisfaction of seeing his 
discovery generally recognised. Des- 
cartes abroad took Harvey's part in 
his letter to Beverwijck in 1637, and 
in his * Discours de la M^thode,' pub- 
lished in the same year ; and it is 
noteworthy that — as has been the 
case with many subsequent English 
discoveries — the first great acknow- 
ledgment came from the Continent, 
notably Holland. The acceptance in 
France by the faculties of Paris and 

Montpellier was less rapid, and in 
England it is well known that Lord 
Bacon took no notice either of 
Harvey's discovery or of Napier's 
invention. See James Spedding's 
preface to the " De interpretatione 
Naturae Procemium" in works of 
Lord Bapon, vol. iii. p. 507, &c. ; also 
Harvey's own opinion on Bacon, ibid., 
p. 515. . Hobbes, on the other hand, 
'* was eager to accept Harvey's revo- 
lutionary discovery " (Croom Rob- 
ertson, * Hobbes,' p. 123), and refers 
to Harvey in the dedication of the 
*De Corpore' (1655) as "the only 
man I know that, conquering envy, 
hath established a new doctrine in 
his lifetime" (ibid., p. 187 n.) On 
Harvey's other works, notably on 
the work ' De Generatione,' see, inter 
aliay Huxley, * Science and Culture,' 
1888, p. 333, &c. 

2 John Ray, or Raj us, as he is 
called abroad (1628-1705), a native 
of Essex, was a Cambridge man ; 
he, however, gave up his fellowship 
in 1662, feeling himself unable to 
subscribe to the Act of Uniformity 
of 1661. He was one of the first 
great classifiers of plants; he col- 

lected a vast amount of information, 
beginning with the neighbourhood 
of Cambridge and extending it in 
travels over Great Britain and the 
Continent with Willoughby. The 

* Historia Plantarum ' — describing 
18,625 species of plants — appeared 
from 1685 to 1704 in 3 vols. The 
first volume contains a chapter on 
the anatomy and physiology of 
plants, which was much extolled 
by Cuvier and recommended for 
republication. The " Ray Society," 
started in 1844 " for the pub- 
lication of works on Natural His- 
tory," brought out among many 
other excellent and celebrated 
works (such as Darwin's * Mono- 
graph of the Family Cirripedia '), 
Memorials (1844) and Correspond- 
ence (1848) of John Ray : it also 
translated that eccentric specimen 
of the "Naturphilosophie" Oken's 

* Elements of Physio - philosophy,' 
1847. A contemporary of John Ray 
was Nehemiah Grew (1628-1711), 
one of the first to make extensive 
use of the microscope (invented in 
Holland between 1590 and 1600) 
for the examination of the anatomy 
and physiology of plants. After 
Oldenburg he was Secretary of the 
Royal Society together with Hooke. 
The Society printed his 'Anatomy 
of Plants.' About the same time 
it seems to have exhausted its 
funds in printing Willoughby's 

* Historia Piscium,' so that it was 
unable to carry out its design of 
defraying the cost of printing the 

* Principia. ' This was generously 
done by Halley. See Weld, ' His- 
tory of the Royal Society,' vol. i. 
p. 309, &c. 

^ Beneath the strife of the Wer- 
nerians and Huttonians, or the 
Neptunists and Plutonists as they 

were termed, the real merits of 
Robert Jameson (1774-1854) and 
James Hutttm (1726-97) have 
sometimes been overlooked. Both 
were ardent naturalists who spent 
their lives in observation and study 
of nature. They made Edinburgh 
for some time the centre of geology 
in this country. Jameson was fifty 
years Professor of Natural History, 
founded the first school of Natural 
History in this country (see Cossar 
Ewart's address, quoted by Sir A. 
Grant, * Story of the University of 
Edinburgh,' vol. ii. p. 444), trained 
a number of eminent naturalists, 
among whom are Edward Forbes and 
Grant (i^.^.— The name of Darwin 
must be added with caution, see his 
* Autobiography,' vol. i. p. 44, &c.), 
founded the Edinburgh Museum of 
Natural History, which includes the 
Huttonian collections, and founded 
the Wernerian and Plinian Societies 
of Natural History. James Hutton, 
though not a teacher like Jameson, 
exerted a great influence through 
John Playfair, who popularised his 
views in his * Illustrations of the 
Huttonian Theory of the Earth' 
(1802). It is termed by Geikie a 
* ' classical contribution to geological 
literature." Though the opposition 
of Hutton's theoretical views to 
those of Werner gave him a great 
reputation as a theorist, it is claimed 
for him that he first among geolo- 
gists disclaimed the intention of 
investigating the origin of things, 
and thus put an end to the cosmo- 
gonies of the eighteenth century. 
Such had been promulgated in all 
the three countries by the most 
illustrious philosophers and natural- 
ists, by Burnet, Buffon, and Leibniz. 
On Hutton's great merits see es- 
pecially Huxley, "Essay on Geolo- 






English love 
of nature. 

mist, acquired a world-wide reputation in the latter part 
of the eighteenth century. 

Many other students of nature could be added to this 
list. Perhaps none has acquired greater popular celebrity 
than Jenner.'^ This he acquired through his extraordinary 
discovery, by which he grappled successfully with one of 
the most prevalent and distressing epidemics from which 
former generations had to suffer. The study of animated 
nature, the observation of the sky and the heavens, have 
always been favourite occupations of Englishmen. The 
love of travels abroad and of the country at home has 
favoured a close intercourse with nature. A fickle and 
humid climate invited the superior skill of the agriculturist 
and the gardener, and rewarded them with heavier crops 
and more luxuriant verdure.^ The chill of the long winter 

gical Reform" (1869. Reprinted 
in *Lay Sermons and Addresses,' 
No. 11). He is there considered 
as the first representative of ** Uni- 
formitarianism " against the older 
*' Catastrophism." Uniformitarian- 
ism has been followed by " Evolu- 

^ Edward Jenner (1749-1823), 
one of the greatest benefactors of 
mankind, spent twenty years on 
the farms of Gloucestershire, fol- 
lowing the advice of his friend and 
master John Hunter, " Don't think, 
but try," before he undertook the 
first inoculation of cowpox on the 
14th of May 1796. About the end 
of the century the process of vacci- 
nation, which dispelled the older 
process of inoculation — introduced 
into England by Lady Fary W. 
Montagu in 1721 — had become 
generally known in Europe. The 
governments of the Revolution in 
France and the Academy of Sci- 
ences had at the end of the century 
occupied themselves a good deal 

with the cure of smallpox, both Vol- 
taire and d'Alembert having taken 
great interest in the subject. 

^ The yield of an acre in wheat 
is in England about 30 bushels or 
one ton of grain ; next comes Bel- 
gium, then Germany, then France ; 
the average yield in the United 
States of America is barely one- half 
of that in England. The yield of 
an acre in Scotland exceeds slightly 
that in England. In Scotland farm- 
ing is carried on with much skill 
and enterprise, and, in spite of the 
severe climate, gardening is prob- 
ably further developed there than 
in any other country. It appears 
that the first voluntary organisa- 
tion for the improvement of agri- 
culture was the "Society of Im- 
provers in the Knowledge of Agri- 
culture in Scotland" formed in 
1723, of which the Earl of Stair 
was one of the leaders. Though it 
counted 300 members, it was short- 
lived : its * Select Transactions * 
were published by Maxwell in 1743. 


Stimulated active exercise and outdoor sport ; the abun- 
dant rains, which fed the many rivulets with a constant 
supply of fresh water, suggested the cultivation of that 
pastime of which Izaak Walton had left a classical de- 
scription, long before Kousseau in France made the love 
of nature a fashionable sentiment. Lord Bacon pointed 
to the study of natural phenomena as the only source 
of knowledge. Evelyn wrote a treatise on forest-trees, 
and the old-fashioned English flower-garden is immor- 
talised in Bacon's 'Essays,' in the "Winters Tale," in 
Cowper's '' Task," and in the works of many other poets. 
Through the literature of the eighteenth century there 
runs a vein of increasing love and knowledge of natural 
objects and natural scenery, beginning in Thomson and 
Gray, widening and deepening in Erasmus Darwin and 
Cowper, and attaining full vigour and originality in 
Burns and Wordsworth, as also in the school of English 
landscape-painting. William and Caroline Herschel com- 

Next came the Bath and West of 
England Society, 1777 ; the High- 
land Society, 1784; and the Na- 
tional Board of Agriculture, 1793. 
The 'Farmer's Magazine' was start- 
ed in 1800. About the same time 
that Lawes and Gilbert in England 
and Liebig in Germany gave such 
an impetus to scientific farming 
through their experiments and pub- 
lications, " Mr John Finnie at Swan- 
ston, near Edinburgh, having sug- 
gested (1842) to some of his neigh- 
bours the desirableness of obtaining 
the aid of chemistry to guide far- 
mers in many departments of their 
business, the hint was promptly 
acted upon, and these Mid-Lothian 
tenant-farmers had the merit of 
originating an Agricultural Chem- 
istry Association (the first of its 

kind), by which funds were raised, 
and an eminent chemist engaged " 
('Ency. Brit.,' article "Agricul- 
ture," vol. i. p. 305). There is pro- 
bably no country where farming is 
such a favourite pursuit of gentle- 
men of leisure and wealth as Great 
Britain, or where the intelligence 
of higher society and of the univer- 
sities is so liberally transferred to 
the benefit of the country, of its 
population, its crops, and its live- 
stock. Among many examples of 
the past and present I mention as 
an outcome of this spirit the little 
volume by Sir Thomas Dyke Ac- 
land, * On the Chemistry of Farm- 
ing' (London: Simpkin & Co., 
1891), and his liberal patronage 
of agriculture in the west of Eng- 





menced the long line of amateur star-gazers of this 
country ; Luke Howard's study of clouds drew from the 
kindred spirit which lived in the great Goethe a loving 
memorial ; ^ and John Dal ton was induced by the mists 
and fogs of his native lake country to join in the foun- 
dation of the modem science of meteorology. 
48. We now discover the reason why the strong individual - 

Union of in- . o i t-« t i i i • i i j 

dividiiaiiam ism 01 the English character, which prompted new de- 

and natural- ^ 

En^ la d- P^rturcs and inspired new ideas in science, as it produced 
adventures and novel enterprise in life and arts, has not 
more frequently led to discouraging failures in the latter, 
or to eccentricity and dreaminess in the former; why it 
has, on the whole, alike in practical work and in scientific 
study, been rewarded by signal success. The rare genius, 
gifted with the power of original thought, who found no 
academy ready to call him, no schools where he could be 
trained, no university eager to nurse and develop his- 

1 Luke Howard (1772-1864), a 
member of the Society of Friends, 
was one of the many lovers of nature 
and amateur naturalists of this 
country in whom new sciences — like 
that of meteorology — are nursed 
during their unpretentious infancy. 
He himself gave a simple narrative 
of his life and doings to the great 
Goethe, who, attracted by his at- 
tempted classification of clouds 
(about 1802, published in his 'Cli- 
mate of London'), had addressed 
some lines to him, accompanying 
them by a statement in verse of 
Howard's description of the stratus, 
cumulus, cirrus, and nimbus : — 

"Er aber, Howard, giebt mit reinem 

Uns neuer Lehre herrlichsten Gewinn : 
Was sich nicht halten, nicht erreichen 

Er fasst es an, er halt zuerst es fest ; 

Bestimmt das Uubestimmte, schrankt es 

Benennt es treffend !— Sey die Ehre Dein t 
Wie Streife steigt, sich ballt, zerflattert, 

Erinnre dankbar Deiner sich die Welt." 

Goethe subsequently tried to get 
some information about Howard's 
way of life, "so that I might see 
how such a mind is formed, what 
opportunities, what circumstances, 
have led him ^into ways of looking 
at Nature naturally, have taught 
him how to devote himself to her, so 
as to find her laws and to prescribe 
these again to her in a natural human 
manner." In his autobiographical 
narrative (reprinted in the last vol- 
ume of Goethe's Works) Howard 
refers to the meteoric phenomena 
of 1783, mentioned also in Cow- 
per's Letters (13th June 1788), and 
White's * History of Selbome. ' 

talent, did not retire into the depths of his own con- 
sciousness, or surround himself with the artificial at- 
mosphere of erudition. The result of such a process 
can be abundantly traced in other countries and other 
literatures. In England the isolation from society and 
the solitariness of genius threw him into the arms of 
Nature, and she has in many instances, in science, in 
poetry, and in art, rewarded and refreshed him by a 
novel inspiration — she has lifted her veil to his loving 
eye and revealed to him one of her secrets. The in- 
dividualism of English science has been tempered by 
its naturalism. A type of this peculiar form of the 
naturalist was Gilbert White, the natural historian of 

^ A long list might be given of 
these retired nature -loving souls, 
among whom Charles Darwin will 
always rank as the greatest and 
most conspicuous. I give here a 
few names in addition to those 
mentioned in the text. 

John Gough of Kendal (1757- 
1825) might, according to John 
Dalton (see his Life by Henry, pp. 
9 and 10), "be deemed a prodigy 
in scientific attainments. . . . De- 
prived of sight in infancy by the 
smallpox, . . . possessing great 
powers of mind, he bent them 
chiefly to the study of the physical 
and mechanical sciences. It was he 
who first set the example of keeping 
a meteorological journal at Kendal ; 
... he knew by the touch, taste, 
and smell almost every plant within 
twenty miles ; he could reason with 
astonishing perspicuity on the con- 
struction of the eye, the nature of 
light and colours, and of optic 
glasses," &c., &c. For about eight 
years Dalton and he were intimately 

George Edwards (1694-1773) of 
Stratford, Essex, was the author of 
the 'History of Birds,' which he 
published between 1743 and 1764 
in six volumes. He had journeyed 
through France and other countries, 
and gave engravings of six hundred 
subjects not before delineated by 

Still more remarkable was Thomas 
Edward (1814-86), the shoemaker 
of Banff, who, having been turned 
out of three schools for his zoolo- 
gical propensities, without friends, 
without a single book on natural 
history, not knowing the names of 
the creatures he found, gained a 
knowledge unique in its freshness 
and accuracy. At the University 
of Aberdeen, where he exhibited 
his collections, he was told by the 
professors that he came "several 
centuries too soon," as they had 
then no chair of Natural History. 
His life has been written by Smiles, 

Edward Forbes (1815-54) of 
Douglas, Isle of Man, a born lover 






White of 

Not long after Eay and Linnaeus had attempted the 
artificial and logical classification of living beings, and 
about the same time that BufPon in France infused into the 
literature of his country a somewhat pretentious love of 
nature, Gilbert White, in a simpler and more healthy style, 
betook himself to describe the aspect that nature presented 
when viewed from the quiet home of an English country 
parson. He may be said to have represented that other 

of nature, "led an unusually full 
life, occupied in promoting science 
and arousing enthusiasm and awak- 
ening intelligence in others. To 
almost every department of biology 
he rendered much service, especially 
by connecting various branches to- 
gether and illustrating one by the 
other. Though his published works 
have been few, his ideas have been 
as the grain of mustard-seed in the 
parable" ('Dictionary of National 
Biography '). After holding various 
badly paid ofl&ces in London and 
elsewhere, he succeeded Robert 
Jameson as Professor of Natural 
History at Edinburgh (see * Memoir 
of E. Forbes,' by G. Wilson and A. 
Geikie, 1861). 

Hugh Miller (1802-56), the self- 
taught stonemason of Cromarty, 
combined the soul of an artist with 
that of a naturalist. His writings 
occupy a place by themselves in 
English Literature. "The principal 
scene of his own investigations was 
the Cromarty district, where he 
ransacked every wrinkle of the hill- 
side, and traced every stratum sawn 
through by the watercourse, and 
where on the beach at ebb, in in- 
durated clay of bluish tint and 
great tenacity, belonging to the old 
Red Sandstone formation, he dis- 
covered and dug out nodules which, 
when laid open by a skilful blow of 
the hammer, displayed organisms 
that had never been seen by the 
human eye." In September 1840 

there appeared in the * Witness ' a 
series of articles entitled " The Old 
Red Sandstone." They formed the 
nucleus of a book of this title which 
established the reputation of Miller 
as an original geologist, as a prac- 
tical thinker and fascinating writer. 
*My Schools and Schoolmasters' is a 
masterpiece of the English language. 
" In an age prodigal of genius, yet 
abounding also in extravagance, 
glare, and bombast, the self-edu- 
cated stonemason wrote with the 
calmness and moderation of Addi- 
son." "The fossil remains seem 
in his glowing pages to live and 
flourish, to fly, swim, or gambol, or 
to shoot up in vegetative profusion 
and splendour, as in the primal 
dawn of creation" (Carruthers, 
quoted by Peter Bayne in *The 
Life and Letters of Hugh Miller,' 
2 vols., 1871). 

David Robertson, the naturalist 
of Cumbrae in the Firth of Clyde 
(born in 1806), was a farm-labourer 
till he was twenty - four, then 
took to the study of medicine, 
and had afterwards for many 
years a china and hardware shop 
in Jail Square, Glasgow. He 
gained a sufficient independence to 
be able to retire in 1860 to Great 
Cumbrae, where he devoted the 
rest of his life to a study of nature. 
Especially in "the marine section, 
by his own unaided efforts, he 
opened up in a remarkable degree 
the zoology of the Firth of Clyde. 

side of natural science, which does not try to comprehend 
nature through the artificial arrangement or classification 
of a museum, but in those connections, among her own 
animate and inanimate objects, which constitute reality, 
and are the characteristics of life and development. It 
was the real, not the artificial, Jardin des Plantes, 
where he and his successors tried to study natural 
objects and the habits of living beings.^ Another re- 

Many animals, till then accounted 
rare, are now known to exist as 
common objects, while the annals 
of science have received many im- 
portant additions of animals alto- 
gether new to natural history 
records — discoveries which have 
caused the Firth of Clyde, and more 
particularly the Cumbrae Islands, 
to become one of the best explored 
and most widely known districts 
of Britain " (Gray, Secretary of 
the Glasgow Natural History So- 
ciety, quoted by Thomas R. R. 
Stebbing in his * Naturalist of Cum- 
brae,' London, 1891). 

William Pearson (1767-1847) of 
Borderside, Crosthwaite, near Ken- 
dal, was a self-educated yeoman, 
who after many years spent in a 
bank at Manchester retired to a 
small patrimonial estate on the 
southern border of Westmorland. 
He possessed a choice collection of 
books, representing fully the English 
poets of all ages, and in translation 
the best German authors. "Of 
the habits of birds and other native 
creatures around him he was a 
watchful observer, and he described 
them in purest English with a 
charm that suggested no disadvan- 
tageous comparison with White of 
Selborne " (see Groves, ' Life of 
Hamilton,' vol. iii. p. 15). He was 
a friend of Wordsworth. 

To this list, which could be in- 
definitely extended, I might add 
another, beginning with Thomas 

VOL. I. 

Bewick (1753-1828), the reviver of 
wood - engraving in England, who 
lent his art and life to the delinea- 
tion of nature. * British Birds ' 
(1797-1804) is a standard work on 
the borderland of art and science, 
in which many other British artists 
have, in humbler or more extensive 
fields, laboured with so much faith- 
fulness and success. 

^ The ' Complete Angler ' and the 
'Natural History of Selborne,' are 
types of a class of literature peculiar 
to this country. In these classical 
productions we are introduced into 
the nursery of English thought, po- 
etry — nay, of science itself. These, 
as the nation draws ultimately its 
wealth from the produce and culture 
of the land, on their part receive 
valuable ideas from a study of 
nature. The purity and origin- 
ality of English art and poetry have 
their home in the same region. 
Gilbert White (1720-93) was born 
and lived in the little Hampshire 
village of Selborne. He was one of 
five brothers, all of whom, in vari- 
ous positions and vocations of life, 
followed the study of nature in its 
minute and local aspects, combining 
with it an antiquarian taste. He 
may not only be classed with the 
naturalists, but belongs also to that 
class of writers, peculiar also to Eng- 
land, who devote their time to the 
compilation of local records, of 
county histories, and to the preser- 
vation of the relics and memorials 





action against the theorising methods which had come 
over from the Continent led to the formation of the 
Geological Society in the year 1807. At that time 
the war of the Wernerians and Huttonians, or, as they 
were also called, the Xeptunists and Plutonists, was rag- 
50. ing in the northern metropolis. The Geological Society 

TheGeologi- ^ . ti ij.- ^ A 

cai Society, of London was established with a view to multiply and 
record observations, and patiently to await the result at 
some future period — that is, its founders resolved to apply 
themselves to descriptive geology, thinking the time not 
come for that theoretical geology which had then long 
fired the controversial ardour of Neptunists and Plu- 
tonists." ^ Fifty years after the formation of this society 

of country life in bygone centuries. 
The series of letters written be- \ 
tween the years 1765 and 1787 ! 
containing ' ' the observations of | 
forty years," and published, 1789, 
with the title ' The Natural History 
and Antiquities of Selborne,' had 
the object "of laying before the 
public his idea of parochial history, 
which, he thinks, ought to consist 
of natural productions and occur- 
rences as well as antiquities." To 
him "nature is so full that that dis- 
trict produces the greatest variety 
which is the most examined." He 
early insists on the necessity of 
monographs in natural history ; 
suggests the usefulness of a " full 
history of noxious insects"; gives 
in a series of letters a faithful and 
minute description of the swallow 
tribe as they are found in his 
country ; traverses the Downs of 
Surrey with a loving eye a hundred 
years before they became celebrated 
through the greater Darwin ; makes 
valuable observations about "earth- 
worms," suggesting a monograph 
on them ; suggests, in an age which 
was governed by the systematising 

mania, that *'the botanist should 
study plants philosophically, should 
investigate the laws of vegetation, 
should promote their cultivation, 
and graft the gardener, the planter, 
and the husbandman on the phy- 
tologist," as "system should be 
subservient to, not the main object 
of, pursuit." 

1 "The one point the catastro- 
phists and the uniformitarians 
agreed upon when this society was 
founded was to ignore it [viz.y geo- 
logical speculation]. And you will 
find, if you look back into our re- 
cords, that our revered fathers in 
geology plumed themselves a good 
deal upon the practical sense and 
wisdom of this proceeding. As a 
temporary measure I do not pre- 
sume to challenge its wisdom ; but 
in all organised bodies temporary 
changes are apt to produce per- 
manent effects; and as time has 
slipped by, altering all the condi- 
tions which may have made such 
mortification of the scientific flesh 
i desirable, I think the effect of the 
stream of cold water which has 
steadily flowed over geological specu- 

the author from whom I quote, Dr Wheweil, in the third 
edition of his ' History of the Inductive Sciences/ could 
still say that "their task was not yet finished, their mis- 
sion not yet accomplished — that they had still much to 
do in the way of collecting facts ; and in entering upon 
the exact estimation of causes, they have only just thrown 
open the door of a vast labyrinth which it may employ 
many generations to traverse, but which they must needs 
explore before they can penetrate to the Oracular Chamber 
of Truth." ^ One of the many individuals in this country 
who " had long pursued his own thoughts without aid and siiVth, 
without sympathy " ^ was William Smith. " No literary 



lation within these walls has been 
of doubtful beneficence" (Huxley 
on "Geological Reform," Address 
to the Geological Society, 1869 ; 
reprinted in 'Lay Sermons,' &c., 
1891, p. 207). 

1 See Wheweil, 'History of the 
Inductive Sciences,' 3rd ed., vol. iii. 
pp. 428, 518. Lyell, * Principles of 
Geology,' 3rd ed., vol. i. p. 102, &c. 

^ Wheweil, loc. cit., vol. iii. p. 
427. William Smith (1769-1839), 
a native of Oxfordshire, has been 
called the Father of English Geo- 
logy. He was — like so many other 
naturalists of this country — an 
a;mateur in his scientific studies, 
which were conducted on the occa- 
sions of his elaborate surveys of 
Oxfordshire, Warwickshire, and 
Somersetshire in connection with 
the engineering of several canals. 
He initiated in England the science 
called on the Continent "Strati- 
graphy," observed the successive 
layers in the geological structure 
of the country, and in 1799 pre- 
pared a tabular view of the order 
of the strata and their organic 
remains in the neighbourhood of 
Bath. For many years after this 

he was occupied in preparing his 
Geological Map of England and 
Wales, which appeared on the five 
miles to the inch scale in 1815 in 
fifteen sheets. He was popularly 
known as " Stratum Smith," but 
remained almost unknown abroad, 
as he himself also seems to have 
taken little notice of Continental 
geology or prevailing theories. 
Though he began earlier than Cu- 
vier and Brongniart, they antici- 
pated him by publishing in 1811 
their mineralogical description of 
the Paris Basin, thus becoming the 
founders of the science of palaeon- 
tology (see Peschel, 'Geschichte 
der Erdkunde,' Miinchen, 1877, p. 
714, &c.) Of the Geological Map 
Lyell says ('Principles of Geology,' 
vol. i. p. 101) that it "remains a 
lasting monument of original talent 
and extraordinary perseverance ; for 
he had explored the whole country 
on foot without the guidance of 
previous observers or the aid of 
fellow-labourers, and had succeeded 
in throwing into natural divisions 
the whole complicated series of 
British rocks." 






Charles BelL 

cultivation of his youth awoke in him the speculative 
love of symmetry and system ; but a singular clearness 
and precision of the classifying power, which he possessed 
as a native talent, was exercised and developed by exactly 
those geological facts among which his philosophical task 
lay. Some of the advances which he made had been 
entered upon by others who preceded him; but of all 
this he was ignorant, and perhaps went on more steadily 
and eagerly to work out his own ideas from the persuasion 
that they were entirely his own." In what he did and 
published, beginning with the year 1790, "we see great 
vividness of thought and activity of mind unfolding itself 
exactly in proportion to the facts with which it had to 
deal." ^ 

About the same time that geological studies received a 
great impe'tus in this country from two distinct centres — 
the philosophical teaching in the Scotch metropolis, and 
the more empirical labours of the Geological Society — a 
signal discovery in another line marked a great step in 
anatomy and physiology. This was Charles Bell's dis- 
covery, in the year 1807, of the difference between sensory 
and motor nerves, "doubtless the most important accession 
to physiological knowledge since the time of Harvey." ^ 

1 Whewell, loc. cit., p. 423. 

2 This statement, taken from Dr 
Henry's ' Report of the British As- 
sociation,' vol. vi., and repeated by 
Whewell {loc. cit, vol. iii. p. 352), 
probably requires a correction, since 
Du Bois-Reymond and others have 
placed in their true historical posi- 
tion the great merits of Descartes, 
who by the discovery of the principle 
of "reflex action" "did for the 
physiology of motion and sensation 
that which Harvey had done for 

the circulation of the blood, and 
opened up that road to the me- 
chanical theory of these processes 
which has been followed by all his 
successors" (Huxley in ihis address 
to the British Association at Bel- 
fast, 1874; reprinted in * Science 
and Culture, &c.,' p. 200, &c.) The 
first enunciation of the principle of 
reflex action had been variously 
ascribed to Joh. Miiller, Prochaska, 
Willis, till Du Bois-Reymond in his 
most interesting ' Gediichtnissrede 

Bell's career was a unique one. He had early severed 
his connection with the great medical schools of Edin- 
burgh, where his brother taught. He lectured and prac- 
tised privately in London, where he gained a considerable 
reputation ; but in his case also it was on the Continent 
that his greatness was more generally recognised. As in 
Dalton's case, his countrymen were slow to do him justice.^ 
In France he had so great a name that a celebrated 

auf Joh. Miiller' (Berlin Acad., 
1859) showed how the merit of 
enunciating it is due to Descartes, 
whose tract on 'Les Passions de 
I'Ame' was published in 1649. 
Both Du Bois-Reymond and Huxley 
give full extracts from the writings 
of Descartes. There seems, however, 
to be some doubt to what extent 
Descartes substantiated his mechan- 
ical view of the action of the nei-v- 
ous system by actual experiments. 
Richet in his 'Physiologic des 
Muscles et des Nerfs' (Paris, 1882, 
p. 505, &c.) refers to this, and 
while giving Descartes his due, 
also says that practically from the 
time of Galen to Charles Bell no 
marked progress had been made 
in the knowledge of the nervous 
system, and that this belongs al- 
most entirely to the nineteenth 
century (pp. 502, 507, 514). Huxley, 
who takes a much higher view of 
the merits of Descartes, says he 
was not only a speculator, but also 
an observer and dissector {loc. cit.^ 
p. 201), and actually places him 
at the head of modem physiology 
(p. 334, &c.) 

1 Charles Bell (1774-1842) was 
bom at Edinburgh. His elder 
brother, John Bell (1763-1820), 
who was a lecturer of great repute 
in the extra-mural School of Surgery 
at Edinburgh, first drew his atten- 
tion to the medical profession. It 
■was only late in life, and after he 

had gained his European renown, 
that he was appointed to the Chair 
of Surgery at the University of 
Edinburgh, which had been created 
in 1831, and it does not appear 
that he was at all sufficiently ap- 
preciated in this position : he used 
to say, " I seem to walk in a city of 
tombs," being unknown in the city 
of his birth (see Sir A. Grant, 
' University of Edinburgh,' vol. ii. 
p. 453). Whilst Charles Bell es- 
tablished the difference of sensory 
and motor nerves, and dispelled 
"the confusion which prevailed up 
to that time in the minds of anato- 
mists and physiologists regarding 
the functions of the various nerves,'* 
the merit of proving by strict ex- 
periment the correctness of Bell's 
theorem belongs to Johannes Miiller 
(1831), who showed it in the frog, 
and to Magendie and Longet, who 
succeeded in exhibiting it in warm- 
blooded animals. Up to the date 
of Miiller's experimental proof no- 
body regarded "Bell's doctrine as 
more than an ingenious and indeed 
plausible, but nevertheless not suf- 
ficiently demonstrated, idea" (see 
Du Bois-Reymond, ' Reden,' vol. ii. 
p. 176, &c. ; also Henle's descrip- 
tion of the demonstration given by 
Miiller in Paris on the 13th Sep- 
tember 1831 to Humboldt, Dutro- 
chet, Valenciennes, and Laurillart, 
in 'Jacob Henle,' by Merkel, 1891, 
p. 83). 






anatomical professor, when Bell visited his lecture-room, 
dismissed his class with the words, " C'est assez, messieurs, 
vous avez vu Charles Bell." 

In Germany one of the great achievements of Johannes 
Miiller, through which he acquired European celebrity, 
was his actual experimental proof of Bell's thesis, with 
which he had occupied himself for many years. 

Instances might be indefinitely multiplied, showing the 
individual greatness, but also the isolation, of English 
men of science and their discoveries ; how the latter ema- 
nated so frequently from the depths of original genius 
in intimate communion with nature ; how they as fre- 
quently lacked those social advantages, that organisation 
for development, which the great schools and establish- 
ments of the Continent all through the century have pos- 
sessed in so eminent a degree. Not only in the study 
of nature has this individual character of British research 
shown itself, though it is here most conspicuous. In the 
exploration of foreign lands and the monuments of by- 
gone civilisations — in the historical branches of research, 
we meet with similar pioneer work. Who does not recall 
the names of Dr Young and of Layard ? I will mention 
only one instance of this kind, where individual ability 
joined to fortuitous circumstances laid the foundation of 
a new branch of research on the borderland of natural 
and political history, the geography of ancient and modern 
G-reece — the exploration of the land which produced the 
most remarkable, and perhaps the most intense, culture 
which the world has yet seen. Note what Ernst Curtius ^ 

says, — the man to whom we are most indebted for the 
systematic historical and artistic study of this remarkable 
country ; whose mind has better than any other succeeded 
in representing to itself the natural and ideal features of 
that country and that bygone race, and who has drawn in 
his writings a series of pictures, reproducing that past 
glory in unequalled perfection. In tracing the begin- 
nings of the modern science of archaeology or historical 
geography, he assigns to England and Englishmen a fore- 
most place as pioneers. " In England there was no medi- 
aeval tradition which suggested expeditions to the East, 
nor did there exist any external occasion or public inter- 
est, but it was a free and purely human attraction which 
led Britons to the classical soil, and private means have 
made all the sacrifices that were required in order to 
satisfy a craving of the soul.^ . . . England became the 

^ See his essay in the 'Preussische 
Jahrbucher,' vol 38, on M. W. 
Leake, and his discourse, *'Der 

Wetteifer der Nationen in der 
Wiederentdeckung der Lander des 
Alterthums" (1880), both reprint- 

ed in that valuable collection, * Al- 
terthum und Gegenwart,' 3 vols., 
Berlin, 1882 and 1889. In the re- 
discovery of the countries of ancient 
civilisation, Italians made the be- 
ginning with Cyriacus of Ancona 
(from 1412 to 1442). Then follow 
the French — Jacob Spon of Lyons, 
a German by birth, being among 
the earliest (1675). The generation 
that succeeded the age of Scaliger 
produced the first maps of Greece 
(Paulmier). Then follows England, 
where the name of Arundel has ac- 
quired a doubtful celebrity through 
that wholesale acquisition of an- 
cient relics which Mr (afterwards 
Sir William) Petty and John Evelyn 
carried on in his name in Greece 
and Asia Minor. It is interesting 
to note here the position that Ger- 
many holds in the growing science 
of archaeology, of which Winckel- 
mann may be considered the foun- 
der. *'The Germans possessed no 

advantages and resources by which 
they could take part in the con- 
test of nations over the rediscovery 
of the countries of ancient history. 
. . . Whilst in Italy it was national 
feeling, in France political relations 
with the East, in England the love 
of collecting and travelling common 
amoDg the aristocracy, which estab- 
lished the connection of the Old 
World with the New, in Germany 
it was the workroom of the profes- 
sor" (Curtius, loc. cit.,\o\. ii. p. 229). 
^ E. Curtius, loc. cit, vol. ii. p. 226. 
"In the year 1742 Stuart and 
Revett wandered among the ruins 
of Rome, and recognised that in 
its relics they beheld only later and 
degenerate forms of ancient art. 
Six years later they set sail for 
Greece. It was, after Cyriacus of 
Ancona and Jacob Spon of Lyons, 
the third journey of exploration ; 
but it was the first in scientific im- 
portance" (p. 227). 









treasury of the wonders of the East, and whilst the Con- 
tinent was closed to her, her travellers flocked to Hellas, 
registering with marvellous patience, watch in hand, on 
the back of the slowly marching mule, piece by piece, the 
remains of antiquity. ... The political mission, headed 
by Martin William Leake, was as such quite unsuccessful ; 
for science, it was of priceless value : from the moment 
that Leake trod on classic soil the reminiscences of Homer 
and Herodotus were kindled, and he saw clearly his life- 
work before him. Under the powerful impressions pro- 
duced by the great table-land of Asia Minor with the 
solitary snow-peak Argaios, deeply moved by the deserted 
places, marching over Grecian inscriptions, over sarcophagi 
and temple ruins, he felt the irresistible charm of the 
attempt to explore and to understand these homes of 
ancient culture.^ ... The scientific result was a lasting 
gain for the civilised world, and the travels which he 
made from 1805 to 1807 mark an epoch in our know- 
ledge of Grecian antiquity."^ 

But the labours of the pioneer in science, life, or art, 
which form so conspicuous an element of this country's 
mental work during the first two-thirds of the century, 
must be supplemented and carried further by a great 
army of patient and trained explorers. Original ideas 
must be cast into an appropriate and elegant form ; new 
discoveries must be extended and criticised by strict 
methods of research; erudition and philosophy are re- 
quired to guarantee completeness and depth. In the 
large domain of the historical sciences these labours of 

1 E. Curtius, loc, cit. , p. 307. 

2 Ibid., p. 312. 

the school and the study are even more important than 
in the exploration of nature, and thus it is not surpris- 
ing that in these especially the bulk of the work, 
though frequently begun by Englishmen, has been car- 
ried on by the great schools and academies of the Con- 
tinent. In the regions of exact science, with which we 
are at present more immediately concerned, there will 
always be a much greater inducement for original minds 
to forsake the beaten track, the recognised method or 

The genius gifted with a larger field of vision and a 
keener glance will always feel the longing to return to 
Nature herself, and the practical man will be allured by 
the prospects of application of science in the arts and 
industries. Both will find their reward ; nor is it likely 
that the works of Faraday and Darwin should be the last 
illustrious examples of great and far-reaching ideas sprung 
from the living intercourse of original genius and nature 
without the support of any school ; or that the practical 
success of the Atlantic cable will be the last fruit of 
the rare combination of highest mathematical genius with 
industrial and commercial enterprise. The historian of 
thought is forced to admit that such rare combinations 
are most likely to spring up amongst a people who have 
always opposed the rule of systems and methods, of schools 
and academies ; who have nursed and cherished an inti- 
mate communion with nature; and for whom practical 
interests and adventures have always preserved an irre- 
sistible attraction. 

Living in an age when the foundation in England and 
in Germany of institutions similar to the Academic Fran- 




Work of 
the three 

Qaise has been seriously discussed,^ when the British 
Association has been copied abroad,^ and when scientific 
men of eminence are joined in conference as to the advis- 
ability of founding a professorial university in London, 
in imitation of the great University of Berlin, it seems 
appropriate to recall the various ways and means by 
which, mainly in this century, the exact spirit of re- 
search, the mathematical method of investigating nature 
iand reality, has been established and diffused. 

France was the country in which the modern scientific 
methods of measurement, calculation, and classification 
were first practised on a large scale, reduced to a system, 
and employed for the investigation of the whole of nature. 
The Academy of Sciences, together with the High Schools 
of Science, the Natural History collections, and Medical 
Institutions, all in close connection, furnished an organi- 
sation of the highest intelligences of the nation, by which 



^ See Matthew Arnold's essay on 
*The Literary Influence of Acad- 
emies,' and Du Bois - Reymond, 
' Uebereine Kaiserliche Akademie 
der deutschen Sprache,' 1874, re- 
printed in *Reden, &c.,' Leipzig, 
1886, vol. i. p. 141, &c. On the other 
side see Huxley in * Critiques and 
Addresses,' ed. of 1890, p. 113, &c. 

^ The British Association, itself 
established somewhat on the model 
of the German '* Naturforscher- 
Versammlung," founded by Oken 
and Humboldt (see supra, p. 238) 
in the year 1831, has become the 
model of the younger "Associa- 
tion fran9aise pour I'Avancement 
des Sciences," founded in 1872 
under the presidency of Claude 
Bernard. It held its first public 
meeting at Bordeaux in 1874. In 
the opening addresses of the presi- 
dent, M. de Quatrefages, and the 

secretary, M. Comu, the elder sis- 
ter in England is referred to. A 
characteristic passage in M. Quatre- 
fages' address as regards the results 
achieved by the British Association 
is the following : * ' Grdce h. elle 
une partie de la population a ^t^ 
transformee. Les fils de ces chas- 
seurs de renards, qui, pour se 
d^lasser de leurs rudes passetemps, 
ne connaissaient que des joies 
^galement violentes et materielles, 
sont aujourd'hui des botanistes, 
des gdologues, des physiciens, des 
archeologues " ('Comptes Rendus,' 
I^re session, p. 40). Following 
the resolutions carried in 1885, 
the French Association amalga- 
mated in 1886 with the older ** As- 
sociation scientifique de France," 
founded by Leverrier in 1864. See 
* Compte Rendu de la 16me Ses- 
sion,' vol. i. p. 1, &c. 

a systematic exploration of the heavens and the earth, 
the inanimate and the living world, could be undertaken. 
At the same time, the methods of measurement and cal- 
culation were submitted to closer study; new sciences 
were created by the application of these methods; and 
problems were attacked for the first time, with which, 
at the end of the century, the scientific world is still 
occupied. It was in France also that the discoveries of 
the laboratory were first applied so as to contribute to 
the revolution of arts and industries. In all its different 
expressions — in the production of works of classical per- 
fection in substance and in form, in its application to the 
problems of life and society, and in its influence on gen- 
eral hterature — we find the scientific spirit, as we know 
it, fully established in France in the beginning of the 
century. About three decades later we find this spirit 
domiciled in Germany, the study of the exact sciences 
having been gradually accepted at the German univer- 
sities as an integral part of the university cycle. It there 
met the philosophical and classical spirit, which had or- 
ganised the German university system and the teaching 
of the higher schools, and had revolutionised historical, 
especially philological, studies. What might have been 
wanting at times in French science, historical complete- 
ness and philosophical criticism, was added in Germany. 
Germany has in the course of this century not only be- 
come the country where the most faithful and exhaustive 
record is kept of the scientific labours of the whole world, 
but it has also become the country where mainly those 
problems have been attacked which lie on the border- 
land of natural science and philosophy, the problems of 









life and consciousness. Modern physiology, especially 
psychophysics, is claimed as essentially a German science. 
Meanwhile England, where the introduction of the 
scientific spirit as an established canon of systematic and 
methodical research was later than in other countries, 
has all through this century, as before, continued to 
do pioneer work in many isolated branches of science : 
individual, as opposed to corporate effort, has here been 
rewarded by a succession of brilliant discoveries, which 
have revolutionised practical life or opened out new 
views into the hidden recesses of nature. For the 
want of organisations of research and teaching, such as 
other countries possessed, these ideas of English thinkers 
have frequently lain dormant or been elaborated by 
foreign talent ; but this want of a recognised system, and 
of a standard course of study, has forced original minds 
into a closer communion with nature and with life, 
whence they have frequently returned to the laboratory 
with quite novel revelations. The largest number of 
works perfect in form and substance, classical for all 
time, belongs probably to France ; the greatest bulk of 
scientific work probably to Germany; but of the new 
ideas which during this century have fructified science, 
the larger share belongs probably to England. Such 
seems to be the impartial verdict of history. During the 
second half of the century a process of equalisation has gone 
on which has taken away something of the characteristic 
peculiarities of earlier times. The great problems of science 
and life are now everywhere attacked by similar methods. 
Scientific teaching proceeds on similar lines, and ideas and 
discoveries are cosmopolitan property. So much more 

interesting must it be for those who have been born 
members of this international republic of learning to 
trace the way in which this confederation has grown up 
what have been the different national contributions to 
its formation, and how the spirit of exact science, once 
domiciled only in Paris, has gradually spread into all 
countries, and leavened the thought and literature of the 






The scien- 
tific spirit 
in the first 
and second 
half of the 


So far I have only treated of the scientific spirit, or of 
the method of exact research, in a general way ; showing 
how it was firmly established and developed in France, 
how it spread into Germany, and received there larger 
and more systematic application, and how in this country 
it gradually and almost imperceptibly grew out of the 
older experimental philosophy. This growth, as we have 
seen, took place partly under the influence of foreign 
science, but still more through the individual and im- 
aided labours of a small number of native intellects of 
the very highest order, to each of whom was for a time 
allotted the enunciation of some specially fruitful idea. 
The period referred to in this survey was mainly the first 
half of our century ; in it were most clearly marked the 
characteristic differences between the three great civilisa- 
tions of France, Germany, and England. A step further 
in time would lead into the midst of our own period — 
into the age which has largely reaped the benefits of those 
earlier labours, both in theory and in practice, fully realis- 
ing in many directions the predictions and even the ideals 



of the pioneers of science. One of these benefits, and 
perhaps that which to an external beholder marks the 
greatest difference between the first and the second half 
of the century, is the greatly increased intercourse which 
now exists as compared with the earlier years of our cen- 
tury. This intercourse has reacted on the domain of 2. 
thought, and produced that exchange of ideas which comelnter- 


promotes more rapid progress. It hardly belongs to the 
history of thought to analyse^ the different steps by which 
the great change has been brought about. Still, a very 
superficial glance will suffice to show how the work of 
bringing about an international exchange of ideas has 
been very characteristically divided among the three 
nations in which we are specially interested. It was not 
in the interest of thought, of science, or of literature, but 
rather in that of commerce and of industry, that the 
modern facihties of intercourse and exchange were in- 
vented and introduced.^ We shall therefore expect to 

^ The principal dates of the in- 
troduction of steam-engines and 
telegraphs for facilitating communi- 
cation are as follows : — 

1802. The tug Charlotte Dundas, 
built by Symington, was tried on 
the Forth and Clyde Canal. 

1812. Henry Bell built the Comet 
with side paddle-wheels. It ran on 
the Clyde as a passenger steamer. 

1829. George Stephenson's Rocket 
was tried on the Stockton and Dar- 
lington Railroad, which had been 
begun in 1821. In the year 1829 
the Liverpool and Manchester Rail- 
way was inaugurated. 

1838. The first steamboats, Sirius 
and Great Western, crossed the 

1833. A comprehensive system of 
railways was planned by the French 
and Belgian Governments. 

1835. The first German railway 
was opened between Niirenberg and 
Fiirth. The first electric telegraphs 
for public use were almost simul- 
taneously constructed in England, 
Germany, and the United States — 
the first successful line being prob- 
ably that constructed by Wheat- 
stone and Cooke between 1836 and 
1840. The first Atlantic cable was 
begun in 1857, and after repeated 
failures, which were in the main 
corrected by the scientific investi- 
gations of William Thomson (Lord 
Kelvin), telegraphic communication 
with America was permanently es- 
tablished in 1866. 

^ This remark applies fully to the 
railway system, but scarcely to the 
development of the electric tele- 
graph, which was first actually used 
for scientific purposes by Gauss and 








find them originate mainly in that coimtry in which 
those larger spheres of practical work had grown un- 
checked and flourished — in Great Britain and its exten- 
sive dependencies. To Germany, on the other side, with 
its fully developed system of learning, we are indebted 
mainly for the complete recording, registering, and analys- 
ing of the scientific labours of the whole world. To France 

Weber at Gottingen in the year 
1833. The documents referring to 
this interesting application have 
recently been published in H. 
Weber's biographical notice of Wil- 
helm Weber, Breslau, 1893, p. 25, &c. 
We read there that soon after 1830 
Gauss had been occupied with re- 
ducing his magnetical measurements 
to an absolute scale, having laid his 
celebrated paper, "Intensitas vis 
magneticae ad mensuram absolutam 
revocata," before the Gottingen So- 
ciety in December of 1832. He had 
induced Weber to take up similar 
investigations at the Physical In- 
stitute, which was situated about a 
mile distant from Gauss's Observa- 
tory. This distance was found to 
be an inconvenience, and in order 
to overcome it, the first longer tele- 
graphic line in which galvanic cur- 
rents were used, and which had 
two wires, was carried overhead 
between the two buildings, and the 
instruments and signalling arrange- 
ments perfected in the years 1833 
to 1836. Both Gauss and Weber 
were well aware of the importance 
of their invention for practical pur- 
poses. The former wrote to Olbers 
on the 20th November 1833: "I 
do not know whether I have already 
written to you regarding a magnifi- 
cent arrangement which we have 
made here. It is a galvanic chain 
between the Observatory and the 
Physical Institute, carried by wires 
in the air over the houses, up the 
Johannis tower and down again. 
The whole length will be about 

8000 feet. ... I have devised a 
simple arrangement by which I can 
instantly reverse the direction of 
the current, which I call a com- 
mutator. . . . We have already 
used this contrivance for telegraphic 
experiments, which succeed very 
well with whole words and short 
sentences. ... I am convinced 
that by using sufficiently strong 
wires one might telegraph instan- 
taneously in this manner from 
Gottingen to Hanover or from 
Hanover to Bremen" (see Scher- 
ing's address on the occasion of 
Gauss's centenary, Gottingen, 1877, 
p. 15, &c.) To Schumacher, 6th 
August 1835, Gauss wrote as fol- 
lows : "With a budget of 150 
thalers [£22, 10s.] annually for 
Observatory and Magnetic Insti- 
tute together, really extensive trials 
cannot of course be made. But 
could thousands of thalers be be- 
stowed thereon, I think that, for 
instance, electromagnetic telegraphy 
might be carried to a perfection and 
to dimensions at which imagination 
almost starts back." Gauss esti- 
mates that fifteen millions sterling 
of copper wire would suffice to reach 
the antipodes, and he says signifi- 
cantly, "I do not think it impos- 
sible to invent a mechanism by 
which a despatch could be played 
off almost as mechanically as a 
musical-box plays off a tune when 
it is once fixed on a roller" (see 
* Briefwechsel zwischen Gauss und 
Schumacher,' ed. Peters, vol. ii. p. 
411, &c.) 


we owe the first beginnings of a general and international 
system of units and measurements, which, like the com- 
mon Latin tongue in former centuries, or like the universal 
languages of algebra or of music, enables us to express the 
results of scientific research in formulae intelligible every- 
where and at all times, without laborious translations and 
time-absorbing reductions. 

The effect of these international labours has been to 3. 
destroy the clearly marked differences of national thought. anSy ' 

. . o national 

At least m the domain of science the peculiarities of the differences. 
French, the German, and the English schools are rapidly 
disappearing. The characteristics of national thought 
still exist ; but in order to find them in the present age 
we should have to study the deeper philosophical reason- 
ings, the general literature and the artistic efforts of 
the three nations. These aspects of the thoughl^iof our 
century belong to later portions of this work. I hope 
there to take up many of the threads which I here break 
off, as for the present purpose they cannot be profitably 
continued. To separate the scientific work of the second 
half of the century according to countries and nations 
would lead to unnecessary repetition. The second half of 
the century sees everywhere in the domain of science the 
dying out of national restrictions — in every country the 
introduction of foreign methods and foreign models, foreign 
institutions and foreign apparatus. The establishment of 
an observatory or a laboratory in our age lays under con- 
tribution almost every civilised country in the world, and 
the most international of sciences — that of electricity — 
fixes its units by the names of discoverers of many 

VOL. I. u 








of science. 

I therefore look upon the spirit of exact research as 
thoroughly domiciled in the leading countries of Europe 
during the second half of the century, and intend in the 
sequel to explain more precisely the different views, the 
leading ideas, under which this research is everywhere 
conducted. These leading ideas have themselves been 
more clearly brought out and recognised during this 


The narrow spirit of the Baconian philosophy which 
reigned in England, the vagueness of the philosophy of 
nature which reigned in Germany, during the earlier 
decades of the century, have disappeared in favour of the 
more comprehensive and the stricter methods taught by 
Lavoisier, by Monge, by Laplace, and by Cuvier in France. 
New ideas of extensive bearing have been added, and in 
the light of these the powers and the limits of science 
have been more correctly recognised. 

To some of my readers well-known names will occur 
which might serve as guides to fix these leading ideas, 
under the influence of which the march of science has 
proceeded: Sir John Herschel, Auguste Comte, John 
Stuart Mill, and Whewell ^ have indeed done much to 

^ Of these writings the earliest is 
Sir John Herschel's "Preliminary 
Discourse on the Study of Natural 
Philosophy," which appeared in 
Lardner's 'Cabinet Cyclopedia' in 
1831. The writings of William 
Whewell on the * History' and ' Phil- 
osophy of the Inductive Sciences' 
were begun about the same time. 
They were planned to serve three 
distinct objects — to give, Ist, a 
philosophical history of astronomy, 
mechanics, physics, chemistry, and 
botany ; 2nd, an analysis of the na- 
ture of induction and the rules of 

its exercise ; and 3rd, to answer the 
question of applying inductive pro- 
cesses to other than material sci- 
ences — as philology, art, politics, 
and morals (see 'William Whewell,' 
by I. Todhunter, vol. i. p. 90). 
The * History' appeared in 1837 in 
three volumes, a second edition in 
1847, a third in 1857 ; the ' Philo- 
sophy ' appeared in 1840 in two 
volumes, a second edition in 1847. 
In the course of its execution the 
original plan was not strictly ad- 
hered to — the scope of the History 
was enlarged considerably, and the 


familiarise the unscientific public with the progress of 
science and its canons of thought. And it would thus 
appear natural to resort to their teaching and their ex- 
planations. But this is not the road I propose to follow. 
Wheweirs ' History of the Inductive Sciences,' being the 
first attempt to compass a large subject, will, like 
Montucla's earlier ' History of Mathematics,' always re- 
main a standard work. It was, however, written at a 
time when the tendency of modern scientific thought was 

Philosophy was broken up into 
different parts. Herschel stands 
mainly on the ground of Bacon's 
philosophy, whereas Whewell starts 
with the remark that " Bacon only 
divined how sciences might be con- 
structed," but that "we can trace 
in their history how their construc- 
tion has^taken place"; that "though 
Bacon's general maxims still guide 
and animate philosophical inquirers, 
yet that his views, in their detail, 
have all turned out inapplicable." 
He accordingly aims at a "New 
Organ of Bacon, renovated ac- 
cording to our advanced intel- 
lectual position and office " (Pre- 
face to 2nd ed. of the 'Philosophy,' 
1847). In the exposition of his 
views Whewell was greatly influ- 
enced by Kant's philosophy. He 
thus searches for the fundamental 
ideas which underlie all scientific 
reasoning ; f or " besides facts, ideas 
are an indispensable source of our 
knowledge." The historical por- 
tions of Whewell's works have met 
with great appreciation in England 
and Germany even from those who, 
like Herschel (see the review in the 
* Quarterly,' June 1841) and Mill 
(see ' Autobiography,' p. 208), could 
not agree with his philosophy. 
The latter has been eclipsed by 
the bolder speculations of Auguste 
Comte, whose 'Philosophie positive' 
appeared in six volumes between the 

years 1830 and 1842 in France. 
Still more than Whewell did Comte 
emphasise the necessity of learning 
from the exact sciences how to 
treat economical and social prob- 
lems in a methodical manner. 
Instead of the minute and fre- 
quently hesitating elaborations of 
Whewell, we find in Comte the 
bold generalisation of the three 
stages of knowledge — the theologi- 
cal, metaphysical, and positive, — 
which forms the groundwork of 
" Positivism." Of more permanent 
value than Whewell's and Comte's 
philosophies are the investigations 
of J. Stuart Mill, who in his ' Sys- 
tem of Logic, Ratiocinative and In- 
ductive' (1st ed., 1843), has laid 
the foundation for all subsequent 
treatises on this subject, and whose 
thoroughgoing empiricism is being 
more and more adopted by scien- 
tific thinkers. Like Whewell and 
Comte, to whom he acknowledges 
his obligations (' Autobiog.,* pp. 165, 
209, &c.), his ultimate object was 
to solve the question "how far the 
methods by which so many of the 
laws of the physical world have 
been numbered among truths irre- 
vocably acquired and universally 
assented to, can be made instru- 
mental to the formation of a similar 
body of received doctrine in moral 
and political science" (Preface to 
let ed.) 

m > 




not as clear as it has become since, and the work has 
also been supers'eded by more detailed labours, espe- 
cially of German historians.^ The * Philosophy of the In- 
ductive Sciences,' by the same author, was written with 
the object of doing something towards determining the 
nature and conditions of human knowledge, and had 
thus a philosophical rather than a historical object in 
view. The same can be said of Mill's ' Logic,' of Comte's 
* Philosophie positive,' and of more recent works — such 
as Jevons's * Principles of Science.' They form an im- 
portant section of the philosophical literature of our 
century, and on future occasions I shall frequently have 
to refer to their teaching. At present I am not about 
to investigate the eternal principles of correct reason- 
ing, and the particular methods adopted, consciously or 
unconsciously, by scientific writers of all times. What 
I desire to do is, to enumerate and analyse briefly the 
changing ideas, the general views, under the guidance 
of which scientific work has progressed in the course 
of this century. No doubt the same object was before 

^ Besides the works on the his- 
tory of the special sciences con- 
tained in the Munich Collection, • 
'Geschichte der Wissenschaften in 
Deutschland,' which in many in- 
stances is not limited to German 
science and learning, there is the 
unique * Geschichte der Chemie,' 
by Hermann Kopp (Braunschweig, 
4 vols., 1843-47), the ' Geschichte 
der Physik,' by Rosenberger (Braun- 
schweig, 3 vols., 1882-90), and 
Haser's * Geschichte der Medicin ' 
(Wien, 1875-82, 3rd ed.) In addi- 
tion to the numerous works of Ger- 
man specialists, I must mention as of 
the first importance and value the 
histories by the late Isaac Todhunter 

of the 'Theory of Attraction and 
Figure of the Earth' (2 vols., 
1873), the * Calculus of Variations ' 
(1861), the 'Theory of Probability' 
(1865), and the 'Theory of Elastic- 
ity' (continued by K. Pearson, 2 
vols, in 3 parts, 1886-93). They 
supply the want of a good history 
of modern mathematics, which does 
not exist. Lastly, the "Deutsche 
Mathematiker - Vereinigung " have 
published in their Jahrbuch valu- 
able histories of special branches of 
mathematics — notably the ' Theory 
of Invariants ' by Franz Mayer, and 
the ' Modern Theory of Functions ' 
by Brill and Noether. 

the mind of Whewell when, after writing his his- e. 


torical work, he attempted in the philosophical sequel 'History, 
to abstract the general ideas which have led scientific osophy.' 
research ; but it is instructive for our present purpose 
to note how, writing about the middle of the century, 
he hardly brought out any of those principles which 
in the course of its second half have turned out to 
be fruitful, and have almost become watchwords of 
popular science. In the year 1857, the date of the 
publication of the latest editions of Whewell's works, 
nothing was popularly known of energy, its conserva- 
tion and dissipation, — nothing of the variation of species, 
and the evolution of organic forms, — nothing of the 
mechanical theory of heat or of that of gases — of 
absolute measurements and absolute temperature; even 
the cellular theory seems to have been popular only in 
Germany. And yet all the problems denoted by these 
now popular terms were then occupying, or had for many 
years occupied, the leading thinkers of that period. But 
we find no mention of them in Whewell's works.^ So 

^ The dates of the birth of these 
leading ideas of the second half of 
our century are approximately as 
follows : — 

Absolute measurements were 
started by Gauss about 1830, and 
the scheme published in 1833' in 
his memoir, ' Intensitas vis magne- 
ticae terrestris ad mensuram absolu- 
tam revocata.' They were extended 
to electrical phenomena by Weber in 
his 'Electrodynamische Maasbestim- 
mungen,' 1846. The absolute scale 
of temperature was introduced by 
William Thomson in 1848. 

The cellular theory was pro- 
pounded by Schleiden in 1838, and 

extended to animal structures by 
Schwann in 1839 ; the term "pro- 
toplasm " was introduced by Mohl 
in 1846. 

The mechanical theory of heat 
dates from Mayer's and Joule's de- 
terminations of the equivalent of 
heat in 1842 and 1843. 

The doctrine of the conservation 
of energy dates from Helmholtz's 
memoir, ' Ueber die Erhaltung der 
Kraft,' in 1847 ; that of dissipation 
of energy from William Thomson's 
paper " On a Universal Tendency 
in Nature to the Dissipation of 
Mechanical Energy," 1852 ; it was 
prepared by Watt's and Poncelet's 




little was the foremost champion of inductive thought 
able to discern the tendencies of his age : a warning to 
those who attempt to recognise the aims of contemporary 

It is not, then, to the philosophical writers that I shall 
apply in order to trace the leading directions of scientific 

definitions of horse- power and work 
(1826), which Whewell does not 

The mechanical theory of gases — 
not to mention the older specula- 
tions of Daniel Bernoulli — dates 
from Avogadro's and Ampere's 
hypothesis, published in 1811, 
" that all gaseous bodies, under the 
same physical conditions, contain 
the same number of units," from 
Herapath (1821) and Joule (1851). 

On Whe well's position with regard 
to the question of the origin and 
variation of species, then already 
ventilated by Lyell, see ' History of 
Induct. Sci.,' vol. iii. p. 489, &c. 
(3rd ed.)> and Huxley's remarks in 
the * Life of Charles Darwin,' vol. 
ii. p. 192, &c. Wallace's essay ' On 
the Law which has regulated the 
Introduction of New Species' was 
published in 1858 along with Dar- 
win's preliminary statement of his 

We might form a whole catalogue 
of scientific terms, some of them 
by no means of recent origin, 
which are wanting in Whewell's 
books, but which now govern scien- 
tific progress : such are energy, 
work, action and eflBciency, absol- 
ute measurement, to mention only 
physical terms. The general ideas 
upon which he himself lays some 
stress, such as those of polarity and 
symmetry, appear on the other 
hand to be vague generalisations, 
which have frequently led people 

^ " It is a remarkable evidence of 

the greatness of the progress which 
has been effected in our time, that 
even the second edition of the 
' History of the Inductive Scien- 
ces,' which was published in 1846, 
contains no allusion to the publi- 
cation in 1843 of the first of the 
series of experiments by which the 
mechanical equivalent of heat was 
correctly ascertained. Such a fail- 
ure on the part of a contemporary, 
of great acquirements and remark- 
able intellectual powers, to read 
the signs of the times, is a lesson 
and a warning worthy of being 
deeply pondered by any one who 
attempts to prognosticate the 
course of scientific progress" (Hux- 
ley in Ward's ' Reign of Queen Vic- 
toria,' vol. ii. p. 355). The same 
writer has pointed out how Au- 
guste Comte was still more un- 
fortunate in his opinions on con- 
temporary science. * ' What struck 
me was his want of apprehension 
of the great features of science ; 
his strange mistakes as to the 
merits of his scientific contempor- 
aries ; and his ludicrously erroneous 
notions about the part which some 
of the scientific doctrines current 
in his time were destined to play in 
the future " (" Scientific Aspects of 
Positivism," 'Lay Sermons,' 1891, 
p. 130). He then goes on to show 
how Comte treated the undulatory 
theory with contempt, extolled 
Gall, depreciated Cuvier, and spoke 
of the "abuse of microscopic in- 
vestigations" (ibid., p. 134). 

thought in our century : their position towards this 
thought is indeed instructive, but it is frequently unsafe. 
Philosophical reasoning either precedes or succeeds 7. 

■^ or Philosophy 

the labours of the scientific, thinker; it rarely accom- and science. 
panies them. In the history of earlier times, during the 
first centuries of the modern period, we find some of the 
foremost philosophers, such as Descartes, Bacon, Leibniz, 
occupied in attempting to lay down the correct lines on 
which science should proceed, or to find general ideas 
which could serve as supreme principles of scientific 
truth. It is a rare thing to find that they have succeeded 
in either of these attempts. In more modern times, 
ever since Locke started on a different track, it has been, 
especially in this country, the endeavour of philosophers 
to abstract out of the existing volumes of scientific re- 
search the leading ideas which have proved so helpful, 
and to explain their origin, their bearing, and their value. 
Perhaps they have been more successful than their pre- 
decessors : it has, however, frequently happened to them, 
that whilst they were elaborately analysing some process 
of reasoning, or some prevailing scientific principle, 
science has meanwhile adopted some entirely different 
line, and presented an entirely unexpected development. 
In this respect they resemble that school of historical 
politicians which in the middle of our century in Ger- 
many ^ attempted to read the signs of the times, and to 

^ This is the school represented by 
the historians Dahlmann and Ger- 
vinus. A good account, wibh a 
somewhat severe criticism of the 
aims of this school, will be found 
in Karl Hillebrand, ' Zeiten, Volker 
und Menschen,' vol. ii. pp. 205-290. 
"The State and Literature had 

grown in Germany alongside of 
each other without • coming into 
contact, the former active, reticent, 
modest, the latter declaiming, 
noisy, pretentious. It appeared as 
if all our life had become intellect- 
ual ; Gervinus himself thought so 
and blamed us. In reality it was 






prescribe the lines on which the desired unification of the 
nation could be secured. Events took their own course, 
and the great statesman who was the central figure of the 
new era of European history may be excused the scorn 
with which he has sometimes treated these theoretical 

The leading ideas which I select as marking the progress 
of scientific research in our century have, with few excep- 

ideas mostly '' 

Sent tions, hardly been discoveries or inventions of this age. 
Some of them are very old. The ideas of attraction, 
which in the hands of Newton and Laplace have led to 
such remarkable results, are of great age, and were 
familiar to the philosophers of Greece and Home ; the 
same can be said of the atomic theory, which in the 
hands of Dalton became such a powerful instrument. 
The principles of energy and its conservation can be 
traced back to the writings of Newton and Leibniz, and 
even to earlier thinkers. The same may be said of the 
* modern ideas on heat, of the molecular theory of gases, 
and even of Lord Kelvin's vortices ; whilst the views 
which through Darwin have revolutionised the natural 
sciences have been traced in the suggestions of much ear- 

not 80. When the professors turned 
their backs on science in order to 
turn to politics, they imagined pol- 
itics were now only beginning : 
with the wonted pride of learning 
they saw in the administrative 
class only labourers and clerks ; for 
to them parliaments and freedom 
of the press were identical with 
politics. The mouthpiece of Ger- 
many was in the universities, as 
that of France was at the bar; 
they only heard each other : was 
it therefore unnatural if they 

thought the German professors 
composed the German nation, as 
the French lawyers formed the 
French nation ? And indeed pub- 
lic opinion in Germany was that of 
the professors. . . . The learned 
newspaper writers imagined the 
spirit of the age spake in them; 
no wonder that th,y overestimated 
the importance of this spirit and of 
this so-called public opinion " (ibid., 
p. 254). See also Treitschke's 
* Deutsche Geschichte,' vol. v. p. 
408, &c. 

lier writers. Elaborate claims to priority have thus been 
set up for persons to whom it is said the credit of modern 
discoveries should be given. I do not intend to contribute 
to this controversial literature, except by a general remark, 
which will explain how it has come to pass that ideas and 
principles now recognised as useful instruments of thought 
and research have only recently attained this importance, 
while they have frequently been the property of many 
ages of philosophical thought, and familiar even to the 
writers of antiquity. It is the scientific method, the exact 
statement, which was wanting, and which raises the vague 
guesses of the philosophical or the dreams of the poetic 
mind to the rank of definite canons of thought, capable of 
precise expression, of mathematical analysis, and of exact 
verificatioM Obscure notions of the attractive and re- 
pulsive forces of nature have floated before the minds of 
philosophers since the time of Empedocles, but they did 
not become useful to science till Galileo and Newton took 
the first step to measure the intensity of those forces. 
Lucretius's poem introduces to us the early speculations 
on the atomic constitution of matter, but the hypotheses 
of his school only led to real knowledge of the things of 
nature when Dalton, following Lavoisier and Eichter, re- 
duced this idea to definite numbers; still more so when, 
through the law of Avogadro and Ampere, and the calcu- 
lations of Joule, Clausius, and Thomson, the velocities, the 
number, and sizes of atoms became calculable and measur- 
able quantities. Descartes, and after him Malebranche, 
filled space with vortices which were to explain the con- 
stitution of matter and the movements of its parts ; but 
the notion was abandoned and ridiculed till Helmholtz 




cal spirit. 

and Thomson approached the subject with mathematical 
analysis and calculated the properties of vortex motion. 

Heraclitus proclaimed, six hundred years before the 
Christian era, the theory that everything moves or flows ; 
but not till this century was the attempt made to work 
out the definite hypothesis of Daniel Bernoulli, and 
to explain the properties of bodies, apparently at rest — 
the pressure of gases, or the phenomena of elasticity — 
by assuming a hidden motion of the imperceptible portions 
of matter. The same fate of lying dormant for ages at- 
taches to the suggestive ideas of many thinkers. (^In every 
case the awakening touch has been the mathematical 
spirit, the attempt to count, to measure, or to calculate.) 
What to the poet or the seer may appear to be the 
very death of all his poetry and all his visions — the cold 
touch of the calculating mind, — this has proved to be the 
spell by which knowledge has been born, by which new 
sciences have been created, and hundreds of definite prob- 
lems put before the minds and into the hands of diligent 
students. It is the geometrical figure, the dry algebraical 
formula, which transforms the vague reasoning of the 
philosopher into a tangible and manageable conception ; 
which represents, though it does not fully describe, which 
corresponds to, though ,it does not explain, the things and 
processes of nature : this clothes the fruitful, but other- 
wise indefinite, ideas in such a form that the strict logical 
methods of thought can be applied, that the human mind 
can in its inner chamber evolve a train of reasoning the 
result of which corresponds to the phenomena of the outer 
world. By such processes did Gauss and Leverrier suc- 
ceed in tracing the lines in the heavens on which invisible 


stars were speeding through the universe ; without them 
these objects of nature would probably never have been 
seen, and if seen, they would not have been recognised. 
Similar, and still more intricate, reasonings permitted 
Mendel^eff^ to arrange in geometrical order the several 
elements or simple substances out of which matter is 
compounded, and to point to the vacant places on the 
chart, some of which have since been filled up by new 
discoveries. Thus it has also been shown that the ranges 
of temperature cannot be extended indefinitely in both 
directions — viz., those of heat and cold — but that the 
latter possesses a zero point, representing the complete 
absence of motion.^ 

^ The periodic arrangement of 
the elements, according to which, 
with increasing atomic or combining 
numbers, the same properties — such 
as density, fusibihty, optical and 
electric qualities, and formation of 
oxides, &c. — recur in periods which 
are at least approximately fixed, so 
that they can be represented by 
curves, dates from the year 1869, 
when D. Mendeleefif and Lothar 
Meyer published almost simultane- 
ously their classification of the ele- 
ments. Newlands seems to have 
indicated some of these facts as 
early as 1864. Mendeleefif pre- 
dicted the properties of a missing 
element, found to be those of scan- 
dium, which Nilson discovered ten 
years later. The same applies to 
the two other elements which were 
subsequently discovered by Lecocq 
de Boisbaudran (1878, gallium) and 
Winkler (1886, germanium), and in 
1894 the newly discovered element 
argon was found to fill a vacant 
place in the plan. 

2 The zero point of temperature 
was originally a purely mathemati- 
cal quantity suggested by the for- 

mula which gives the expansion of 
air in the air thermometer as de- 
pendent on the temperature. The 
ideal, not realisable, temperature 
at which, according to the for- 
mula, the volume of air would be 
nothing, was fixed by calculation at 
459°-13 Fahr. or 272' '85 Centi- 
grade. The real physical, not mere- 
ly mathematical, meaning of the 
absolute scale of temperature with 
its zero point was only revealed 
when, through Carnot and Thom- 
son, it was established that every 
degree of temperature has an assign- 
able value for doing work, and when 
a scale of thermometry was sug- 
gested by Thomson (1848) in which 
every one degree had the same 
dynamical value, 100° in it cor- 
responding to the 100° Centigrade 
in the air thermometer. It was 
then found that the two scales— 
that of the air thermometer and 
that measuring the dynamical value 
of temperature — agreed almost ex- 
actly. The number 273° Cent, thus 
acquired a physical meaning (see 
Clerk Maxwell, 'Heat,' 8th ed., 
pp. 49, 159, and 215). Another 




By drawing curves on paper which correspond to the 
thermal properties of various substances, the conditions 
have been defined beforehand under which gaseous bodies 
like oxygen, hydrogen, nitrogen, or common atmospheric 
air can be reduced to liquid and solid bodies, upsetting 
the notions of the last generation, which looked upon 
these substances as permanent gases.^ If the mathe- 
matical formula has killed, or failed to grasp, the true 
life of nature, that which to the poet and the philosopher 
will always be the feature of supremest interest, it has on 
the other side given birth to that new life of ideas which 
in our reasoning minds serve as the images of things 

example of a purely mathematical 
quantity which, suggested originally 
by a formula, acquired later a physi- 
cal meaning, is that of the potential 
function, used first by Lagrange as 
a simplification in calculating the 
forces of a disturbing planet, and 
termed by Laplace ' ' h, cause de son 
utilite, une veritable decouverte" 
(*Mec. eel.,' v. livre xv. chap, i.) 
This function, which has the pro- 
perty that by a simple differentia- 
tion the component of the force in 
any direction is found, acquired a 
physical meaning as the quantity, 
the change of which measures the 
work required to move a unit of 
matter from one point to another 
(see Thomson and Tait, ' Natural 
Philosophy, ' vol. i. 2, p. 29). Other 
examples of purely mathematical 
quantities which reveal physical 
properties are Hamilton's "char- 
acteristic function " (see Tait, 
"Mechanics," 'Ency. Brit.,' 9th 
ed., p. 749), Rankine's "Thermo- 
dynamic function," called by Clau- 
Entropy " (see Maxwell, 



'Heat,' pp. 162, 189) : it measures 

the unavaulable energy of a system. 

1 Thomas Andrews (1813-85) took 

up the experiments begun by Cag- 

niard - Latour in 1822, and ex- 
plained how it comes about that a 
gas remains incondensable however 
great the pressure may be, pro- 
vided the temperature exceeds 
what he termed the "critical tem- 
perature," which is different for 
different gases. He accompanied 
his statements, which were first 
published in the 3rd edition of 
Miller's Chemical Physics, by curves 
representing the behaviour of at- 
mospheric air and of carbonic acid, 
the latter being a condensable gas, 
and he suggested in 1872 that the 
so-called permanent gases had a 
critical point far below the lowest 
known temperatures, and that this 
was the reason why their lique- 
faction had not yet been achieved. 
Two physicists, Cailletet and Pictet, 
took up these suggestions ; after 
various trials they succeeded inde- 
pendently in 1877 in liquefying 
several of the permanent gases, 
notably oxygen and nitrogen. 
These have been followed by all 
the other permanent gases, includ- 
ing atmospheric air, of which large 
quantities can now be prepared in 
a liquefied form. 

natural, and allow us to make them subservient to our 

Whoever grasps the significance of the change which lo. 

, -1 , 1 • 1 When first 

tne exact or mathematical treatment of knowledge has introduced 

^ into science. 

worked in our life and thought, will readily place that 
name at the entrance of a history of modern thought, 
which is identified with a few simple mathematical for- 
mulae, by which ever since his time the progress of science 
has been guided. Though belonging to an earlier period, 
the full meaning of Newton's work has only been recog- 
nised in the course of our century. In fact the New- 
tonian philosophy can be said to have governed at least 
one entire section of the scientific research of the first 
half of this period : only in the second half of the period 
have we succeeded in defining more clearly the direction 
in which Newton's views require to be extended or modi- 
fied. (Newton's greatest achievement was to combine the 
purely mechanical laws which Galileo and Huygens had 
established with the purely physical relations which 
Kepler — following Copernicus and Tycho — had discovered 
in the planetary motions, and to abstract in so doing 
the general formula of universal attraction or gravitation.) 
Newton looked upon the motion of the moon round the 
earth, or the planets round the sun, as examples on a 
large scale of the motion of falling bodies — studied by 
Galileo — on the surface of the earth. Delayed in the 
publication of this simple rule of planetary motion 
through the absence of correct measurements, and through 
the necessity of inventing a new calculus by which the 
mathematical results of the formula could be ascertained, 
Newton did not publish his 'Principia' till 1687. The 




' Principia/ 

work, however, was conceived in the highest philosophic 
spirit, inasmuch as the enunciation of the so-called law of 
gravitation required the clear expression of the general 
laws of motion. In the first and second parts of the 
work the discoveries of Galileo and Huygens were ab- 
sorbed, generalised, and restated in such terms as have up 
to our age been considered sufficient to form the basis for 
all purely mechanical reasoning.^ In the latter part the 
new rule, corresponding to Kepler's empirical laws, is 
represented as the key to a system of the universe. The 
great outlines of this system are boldly drawn, and the 
working out of it is left as the great bequest of Newton 
to his successors. At the end of the eighteenth century, 

^ The most recent historian of 
the subject is Prof. Ernst Mach of 
Prague, whose 'Mechanik in ihrer 
Entwickelung, historisch - kritisch 
dargestellt,' 2nd ed., 1889, I cannot 
praise too highly. It has been 
translated into English by M'Cor- 
mack (Chicago and London, 1893). 
Referring to Newton, he says : 
" Newton has with regard to our 
subject two great merits. Firstly, 
he has greatly enlarged the hori- 
zon of mechanical physics through 
the discovery of universal gravi- 
tation. Further, he has also com- 
pleted the enunciation of the prin- 
ciples of mechanics as we now ac- 
cept them. After him an essen- 
tially new principle has not been 
established. WTiat after him has 
been done in mechanics refers to 
the deductive, formal, and mathe- 
matical development of mechanics 
on the ground of Newton's prin- 
ciples" (p. 174). "Newton's prin- 
ciples are sufficient without the 
introduction of any new principle 
to clear up every mechanical prob- 
lem wliich may present itself, be 

it one of statics or of dynamics. 
If difficulties present themselves, 
they are always only mathematical, 
formal, not fundamental " (p. 239). 
'*A11 important mathematical ex- 
pressions of modern mechanics were 
already found and used in the age 
of Galileo and Newton. The spe- 
cial names . . . have sometimes 
been fixed much later. Still later 
came the adoption of uniform 
measures, and this process is even 
yet incomplete " (p. 252). In this 
country it is one of the great mer- 
its of Thomson and Tait's 'Nat- 
ural Philosophy ' that they " re- 
stored" the teaching of mechanics 
and placed it on the original foun- 
dations afiForded by Newton's laws 
of motion, in his own words, as 
** every attempt that has been 
made to supersede them has ended 
in utter failure" (Preface), and, 
though they "are only tempor- 
arily the best," there does not 
exist, "as yet, anything nearly as 
good " (Tait in article " Mechanics," 
'Ency. Brit.,' 9th ed., p. 749). 


after many able mathematicians and observers had gen- 
erally investigated the numberless problems contained in 
the 'Principia,' Laplace published his 'Exposition du 
Syst^me du Monde,' followed in the course of the first 
quarter of this century by the ' M^canique celeste ' ; ^ and 
at the close of the present century the most learned 
astronomer of the age could say that the 'Principia' 
still formed the sole foundation of all investigations in 
that domain.^ 

(it is interesting to see how in a simple formula the 12. 
mathematician is able to condense an almost immeasur- SonlSr'^ 
able volume of thought, bringing the theory and the °''^' 
observations of past ages to a focus from which new lines 
of thought diverge in many directions.'^ Every mathe- 

^ The 'Exposition du Syst^me 
du Monde' appeared, 1796, in 2 
vols. 8vo : the first and second 
volume of the * Mecanique cdleste,' 
1799, 4to; the third, 1802; the 
fourth, 1805 ; the last, 1825. Be- 
fore publishing this work, which 
has been termed a second edition 
of the 'Principia,' Laplace had 
himself during thirty years assisted 
in dispelling the last doubts as to 
the sufficiency of the doctrine of 
universal gravitation to explain all 
cosmical phenomena ; and he had 
especially brought the investiga- 
tions of Clairaut, Euler, d'Alem- 
bert, Lambert, and Lagrange to a 
final result by publishing in suc- 
cessive memoirs between 1773 and 
1786 the doctrine of "the stability 
of the system of the universe," 
based upon the invariability of the 
major axes and the periods of re- 
volution of the planetary orbits. 
He and his predecessors also ex- 
tended the solution of the problem 
**to find the orbit of two bodies, 
acting under the law of mutual 

gravitation," which was given by 
Newton in such a way that the 
action of one or more third (dis- 
turbing) bodies could be taken into 
account, dealing thus with the case 
of nature, which had in the first 
instance presented itself in treating 
of the complex motion of the moon. 
Laplace himself, who in number- 
less passages of his works re- 
curs to the discoveries of Newton, 
announced the object of the 'Me- 
canique celeste ' to be the treat- 
ment of astronomy "as a great 
problem of mechanics, from which 
it was important to banish as much 
as possible all empiricism," and to 
perfect it so as "to borrow from 
observation only the most indis- 
pensable data" ('M^c. cdl.,' vol. L 

2 The late Professor Rudolf Wolf 
of Ziirich, whose ' Handbuch der 
Astronomic, ihrer Geschichte und 
Litteratur,' 2 vols., 1890-93, as well 
as his earlier 'Geschichte der As- 
tronomie,' Miinchen, 1877, 1 warmly 




matical formula which expresses the existing relations 
of natural things acts in a similar way, but probably few, 
if any, subsequent discoveries have given scientific minds 
so much fruitful work to do as the gravitation formula. 
An analysis of it will serve us as a guide through a very 
large portion of the scientific work of our period ; it will 
serve also as an example of the great service which the 
mathematical mode of dealing with conceptions renders to 
the progress of science and of thought. 

(The so-called law of gravitation states that every two 
portions of matter, placed at a distance from each other, 
exert on each other an attractive force,^ which depends 
on the masses of each, and on their distance from 
each other. Th6 attractive force varies in the direct 
proportion of the mass of each, and in the inverse 
duplicate ratio of the distance.) Three distinct lines of 


^ The gravitation formula gives 
no indication of the actual or abso- 
lute amount of the force in ques- 
tion ; it only establishes a relation.] 
It was fully three-quarters of a 
century after the publication of the 
* Principia ' that experiments were 
suggested in order to determine the 
actual magnitude of the force of 
gravitation — i.e., the constant c in 

the formula /= c — V-. . Michell in 

1768 devised an apparatus, em- 
ployed later (1797) by Cavendish, 
and Maskelyne made measurements 
towards the end of the last century. 
More and more accurate determin- 
ations were made all through the 
present century, and latterly by 
Prof. Boys. Few persons have an 
idea of the extreme feebleness of the 
force, which nevertheless, through 
the magnitude of the earth, ac- 
quires in our daily experience such 
ormidable proportions. As it is 

desirable, in accordance with one of 
the principal scientific tendencies of 
our age, to place the knowledge of 
absolute physical quantities in the 
place of merely relative numbers, 
I mention here that the force with 
which two units of matter {i.e., 2 
grammes) placed at unit distance 
{i.e.y 1 centimetre) apart attract 
each other is such that they would 
approach each other with a velo- 
city of nearly 7 hundred millionths 
of a centimetre in the first second 
of time. As a pound is a more 
familiar quantity, we may also say 
that two masses, each containing 
415,000 tons of matter, and situ- 
ated at a distance of one statute 
mile apart, will attract each other 
with the force of 1 lb. (see Sir 
R. S. Ball, 'Ency. Brit,' 9th ed., 
art. "Gravitation"). See also Sir 
R. S. Ball, 'The Story of the 
Heavens,' p. 106, and Prof. Boys 
in 'Nature,' vol. 50, p. 330, &c. 

scientific research are involved and opened out by this is. 

. 1 i Lines of 

statement. thought 

_,. _,, . emanati 

J^irst, There is the purely theoretical task of defining ^^°"^**^- 
clearly what is meant by the different words which are 
used, and which in the formula are expressed in algebraic 
symbols. What is the definition of force, what of mass, 
what of distance ? The ' Principia ' give Newton's defi- 

Second, The definitions must be given in such a way 
that they express definite measurable quantities ; and in 
order to verify and apply the formula, methods must be 
devised for measuring these quantities as they occur in 
nature, and these measurements must be actually carried 

^ It will be readily admitted that 
the definition of force as measured 
by change of motion, and the defi- 
nition of mass as the quantity of 
matter, are definitions involving 
some difficulty. As to distance, 
it may be thought that this is a 
purely mathematical, not a physi- 
cal quantity. So it would be if 
physical bodies were mathematical 
points, such as the planets in a 
first approximation may be con- 
sidered to be. But in comparing 
the attraction of the earth upon 
a body at its surface with that on 
the moon, the dimensions of the 
earth could not be neglected, and 
the problem presented itself how 
the quantities of mass and distance, 
in the case of the earth and the 
body on its surface, had to be de- 
fined. It appears from a statement 
by Prof. Glaisher (see Rouse Ball, 

* History of Mathematics,' p. 297, 
&c.) that the publication of the 

* Principia,' containing the gravita- 
tion formula, was delayed, because 
Newton found it difficult to prove 
that in a sphere the different parts 

VOL. I. 

' with their different distances from 
any point need not be considered 
separately, but that a quantity 
equal to the whole mass situated 
at the centre of the sphere may 
be substituted. Laplace showed a 
century later that this property of 
the sphere exists only for one de- 
creasing function of the distance — 
inz., that of the inverse duplicate 
ratio. It exists likewise for that 
function which increases in propor- 
tion to the distance, but for none 
other (see 'Principia,' 1st ed., pp. 
198, 200; 'M^canique celeste,' 1st 
ed., vol. i. p. 143). Hitherto the 
delay in publishing the ' Principia ' 
was (see Brewster, 'Life of New- 
ton,' vol. i. p. 290) always attrib- 
uted to the erroneous figure of the 
moon's distance from the earth, 
with which Newton had been 
reckoning, and which did not sat- 
isfy the gravitation formula. 
I ^ Up to the beginning of this 
century the merit of carrying out 
accurate measurements of astrono- 
mical constants is about equally 
divided between France and Eng- 




Third, the formula is a mathematical expression, and, as 
such, can be subjected to purely mathematical analysis : 
this analysis may refer to purely algebraical processes of 

land; the former country having 
supplied the means and organised 
many expeditions (under Richer, 
Picard, Cassini, La Coudamine, 
Maupertuis, and others), the latter 
having invented and furnished the 
greater portion of the delicate in- 
struments, through Newton, Greg- 
ory, Ramsden, Dollond, Harrison, 
and others. The latter was a 
matter of personal, the former one 
of organised, talent. England did 
not take any great part in the re- 
peated measurements of the arc of 
the meridian till, towards the end 
of the eighteenth century (1785-87), 
the French astronomer Cassini de 
Thury presented to the Royal So- 
ciety a memorial on the uncertainty 
in the difference of longitude of 
Greenwich and Paris, and proposed 
that the English and French mathe- 
maticians in concert should deter- 
mine, by geodetic operations, the 
distance measured along an arc of 
parallel. This was assented to, and 
the late Astronomer Royal (G. B. 
Airy) claims that it *' may be said 
that in this as in other grand ex- 
periments, though we began later 
than our Continental neighbours, 
we conducted our operations with 
a degree of accuracy of which, till 
that time, no one had dared to 
form an idea." Since the begm- 
ning of this century Germany has, 
through the accurate measurements 
of Gauss and Bessel, and through 
the famous establishments of Fraun- 
hofer, Steinheil, Repsold, and others, 
taken a leading position both in the 
theory and practice of measuring. 
So far as gravitational astronomy 
is concerned, the United States of 
America seem at the end of this 
century to eclipse all previous 
performances. But if we owe to 

English genius the invention of 
logarithms, the sextant, the reflect- 
ing and the achromatic telescope, 
the theodolite, and the chrono- 
meter, we owe to France the idea 
of an absolute system of measure- 
ments and the first approxima- 
tion to it in the metrical system, 
which England has been tardy to 
adopt. A really absolute unit of 
measurement, as the ten-millionth 
part of the earth quadrant was in- 
tended to be— one which would be 
recoverable, if every actually ex- 
isting pattern was destroyed— does 
not yet indeed exist; but the 
Government of the Revolution laid 
the foundation in 1790 of our 
present international decimal cen- 
tigrade system. It does not ap- 
pear that the idea of extending this 
system to all other forces and 
quantities in nature was then con- 
templated. A valuable contribu- 
tion towards this desirable object 
was made by Fourier, who in his 
celebrated ' Theorie de la Chaleur ' 
(1822, p. 152, &c.) laid down the 
doctrine of the "dimensions" of 
physical quantities which had to 
be measured and compared with 
each other. The first who reduced 
the measurement of other than 
purely mechanical phenomena to 
the standard of mechanical forces 
was Gauss (1832). In his investi- 
gations referring to the intensity 
of magnetic force at different points 
of the earth, he found it necessary 
to abandon the unit of weight, the 
gramme, and to adopt the unit of 
mass, inasmuch as the weight of 
the unit of mass varied at different 
points of the globe. He introduced 
the name "absolute" to signify 
that this standard is independent 
of local or relative influences (see 


calculation, or to geometrical figures. These geometrical 
figures represent on paper, and on a small scale, the 
curves or orbits of bodies in space and time, and can 
be interpreted as such. Then, as in nature two bodies 
or portions of matter are never single gravitating points 
occurring alone, but are surrounded by the totality of 
existing things, the formula which reduces the action of 
gravitation to that of pairs of things, and to the elements 
of matter, requires to be extended to more than two — in 
fact to an infinity of elements. The infinitesimal calculus 
teaches us how to deal with such a progression from finite 
numbers and quantities to infinite numbers ; or from rela- 
tions which refer to infinitesimal elements to finite meas- 
urable quantities. We find very soon that our powers of 
calculation reach only a small way, and cover only a small 
extent of the ground which observation opens to our eyes. 
We are thus forced to deal with the element of error u. 
which creeps into our calculations ; to be satisfied with f^^^!""^ °^ 
approximations ; ^ and instead of certainty, probability is 

Gauss, Werke, vol. v. pp. 85, 293, 
&c.) Of Weber's electrodynamic 
measurements I shall speak later on. 
Absolute measurements were used 
by William Thomson (Lord Kelvin) 
as early as 1851, and owing mainly 
to his influence the present system 
was gradually established in the 
course of the following twenty years 
(see William Thomson, 'Popular 
Lectures and Addresses,' vol. i. p. 
83, &c.) Fourier's theory of dimen- 
sions was first brought prominently 
before the scientific and teaching 
world by Clerk Maxwell in his trea- 
tise on ' Electricity and Magnetism ' 
(1st ed., vol. i. p. 2). There also 
we meet for the first time with 
the use of astronomical magnitudes 
and relations by which the usual 

three units, time, mass, and dis- 
tance, can be reduced to two. This 
is also lucidly explained by Lord 
Kelvin {loc. cit.} It has been fol- 
lowed up in detail in two interest- 
ing papers by W. Winter in Exner's 
' Repertorium der Physik ' (vol. 21, 
p. 775, and vol. 24, p. 471). 

^ The history of astronomical cal- 
culations since the time of Newton, 
when the theoretical basis was once 
for all laid, is a history of gradual 
approximations. Mathematically a 
conic section is sufficiently defined 
if the position of the focus (the sun 
in our planetary system) and three 
positions of the moving star are 
known by observation. But it was 
a long time before even tolerably 
complete methods of observation 




the best we can attain to in our results.^ An entirely 
new branch of investigation springs up — viz., the theory 
of error, the doctrine of probability, and the investigation 

and calculation were invented to 
deal practically with the problem. 
Up to 1781, when the new planet 
Uranus was discovered by Her- 
schel, the interest centred mainly 
in the determination of the orbits 
of comets, which were assumed to 
be parabolic. Halley was the first 
to calculate these by means of ten- 
tative methods given by Newton in 
the ' Principia.' After 1781 the ne- 
cessity arose of determining closed 
orbits, and a first attempt was made 
to do 80 by assuming circular orbits 
(neglecting the ellipticity) and ne- 
glecting the inclination of the plane 
of the orbit to that of the earth. 
But in the first year of this century 
neither the parabolic nor the circular 
figure of the orbits seemed to an- 
swer in the case of the new planet 
Ceres, nor could the inclination of 
the orbit be neglected. It required 
all the skill of Gauss to teckle the 
entire, unabbreviated problem, and 
this was done in his fundamental 
work 'Theoria motus corporum 
ccelestium.' As the 'Principia' 
form the foundation of all physical, 
so does the 'Theoria motus' of all 
calculating astronomy. A similar 
fundamental work which should take 
the next important step, solving 
generally the problem of the motion 
of a body which is attracted from 
more than one fixed or movable 
centre (the problem of three bodies), 
would mark the next great era in 
calculating astronomy. Hitherto 
this problem has only been treated 
under the assumption that the third 
attracting body disturbs the real 
orbit which has been calculated. 
The necessity of solving the prob- 
lem of three* bodies has made itself 
felt in the theory of the moon and 
other satellites, which stand under 

the influence of the main planet as 
well as the sun, and where therefore 
the ellipsis of Kepler cannot even 
be taken as a first approximation. 
And here again the necessity of tak- 
ing into account the volume and 
the figures of the attracting bodies 
still further complicates the prob- 
lem. On them depend the preces- 
sion of the equinoxes and the ir- 
regularity of the precession known 
under the name of nutation. 

1 According to Wolf (' Handbuch 
der Astronomie,' vol. i. p. 128 sqq.) 
the merit of having first considered 
the best methods of dealing with 
errors of observation belongs to 
Picard (1670) and Roger Cotes 
(* Aestimatio errorum in mixta 
mathesi,' 1722). The former seems 
to have first used the apparently so 
obvious rule of taking the arith- 
metical mean of a number of ob- 
servations, the latter introduced 
the notion of attributing to each 
observation its value or weight. 
Cotes accordingly found that the 
centre of gravity of a number of 
weighted points distributed over a 
plane coincided with the position of 
greatest probability. Gauss sus- 
pected that Tobias Mayer had 
already employed modem methods 
in his calculation of long series of 
observations, and he himself used 
what is termed after Legendre the 
" method of least squares " as early 
as 1795. It was not published till 
1806 by Legendre, in his memoir 
* Nouvelles methodes pour la deter- 
mination des orbites des cometes.' 
Gauss published his methods in 1809 
in the celebrated 'Theoria motus 
corporum ccelestium.' This method 
of finding the most probable result 
when a larger number of equations 
is given than unknown quantities 


of the degree of approximation which we can attain to. 
And this does not only refer to the methods of calculation 
which we adopt, — is not only a consequence of the limits 
of our mathematical powers; this element of error attaches 
likewise to our actual observations, to the imperfection of 
our senses and of our instruments. The many sources 
of mistake and inaccuracy which surround us may either 
combine to produce an absolutely useless result, or may 
be adroitly adjusted so as very largely to destroy each 
other.^ The arrangement of instruments of observation 
and calculation, so as to minimise our errors, is a special 
branch of science. Before the time of JSTewton few minds 

is the same as that of finding the 
centre of gravity of a number of 
weighted points. This centre has 
the property that the sum of the 
squares of its distances from these 
points is a minimum. After the 
method had been introduced, La- 
place and Gauss independently tried 
to prove it by a variety of considera- 
tions. These have not always been 
accepted as conclusive, though it is 
remarkable that very different ways 
of attacking the problem all lead to 
the same result, and that the rule 
is confirmed by actual trials on a 
large scale. It has been shown that 
the method of least squares in the 
case of a series of observations of 
one and the same quantity is equal 
to taking the arithmetical mean, — a 
process which recommends itself to 
common-sense, though it is not easy 
to prove it mathematically to be the 
best. On the whole, the calculus 
of probabilities and the so-called 
law of error are attempts to put 
into figures and mathematical for- 
mulae a few common-sense notions, 
and it is interesting to see to what 
complicated processes of reasoning 
a combination of these simple no- 
tions may lead. The literature of 

the subject, belonging almost en- 
tirely to this century, is very large, 
Laplace and Gauss heading the list. 
Encke has summarised the scattered 
discussions of Gauss and Bessel in 
his memoir on the subject, reprinted 
in Taylor's ' Scientific Memoirs ' and 
in the 2nd vol. of Encke's * Abhand- 
lungen,' Berlin, 1888. De Morgan, 
Airy, and Jevons ('Principles of 
Science,' vol. i.) in England have 
done much to popularise the sub- 
ject, and Bertrand (' Calcul des Pro- 
babilites,' 1888) has very fully dis- 
cussed the principles of the whole 
matter and shown up the weak 
points. The application of the cal- 
culus to statistics will occupy us in 
a future chapter. 

^ Not only has every instrument 
its constant errors, but even every 
observer himself has what is called 
a personal equation — i. e., he is sub- 
ject to constant errors of observa- 
tion, dependent on the peculiarity 
of his sense organs, or his tem- 
perament, &c. This was hardly 
recognised at the beginning of this 
century, when Meiskelyne, the As- 
tronomer Royal, dismissed an as- 
sistant whose observations showed 
a constant difference from his own. 




Laplace and 







were occupied with the many researches indicated here. 
But as the contents of the * Principia ' became familiar 
and intelligible to men of science, a large army of 
workers, collected from all sides, had within the first 
century after its publication accuinulated a great mass of 
research. It is the glory of the old French Academy of 
Sciences, in spite of the opposition to Newton that ruled 
there for some time, to have in all earnest taken up his 
great bequest, and to have made such a summary possible 
as was given by Laplace in the two works above re- 
ferred to. To Laplace belongs also almost exclusively the 
merit of having recognised the importance which attaches 
in all human science to the existence of error, and of 
having founded the theory of probability. The element 
of error cannot be eliminated from our observations and 
our reasonings : the only true scientific method is to 
measure and study it. 

The gravitation formula of Newton not only brought 
precision and definiteness into scientific work in the three 
directions mentioned above — it not only produced strict 
definitions of the fundamental notions of dynamics, pro- 
moted accurate measurements of physical quantities, and 
inaugurated a new literature in pure mathematics ; but it 
had, as all other great generalisations have had since, a 
very far-reaching influence on scientific thought in other, 
ways. There always have been, and always will be, 
several distinct interests which induce men to study 
nature. Some are driven to it by curiosity, or a pure 
love of nature. To those who belong to this class the 
end of the study of nature is to describe and to portray 
the objects which surround us, to see and know them 


better. It would seem as if to such minds the scientific 
formula, the so-called law of nature, must be distasteful, 
and probably useless. Nevertheless the scientific view, of 
which the mathematical formula is an extreme expres- 
sion, has reacted, though not always beneficially, upon 
the labours of those who confine themselves to observa- 
tion and description ; it has given to their efforts general 
interest and encouragement, indicated new directions, and 
frequently opened new fields. Thus the new formula of 
Copernicus and Galileo gave a great impetus to star- 
gazing, which was greatly increased by the almost con- 
temporary invention of the telescope. The new theory 
required the rotation of the planets, and led to minute 
observations of their phases, and to the discovery of the 
satellites of Jupiter and the ring of Saturn. Variable 
stars were incidentally discovered by Tycho, and the 
long-neglected comets received greater attention. Ber- 
noulli attempted, and Halley actually carried out, the 
calculation of the return of a comet. Still later — in 
fact, not before the end of the eighteenth or the beginning 
of the present century — came the turn for reliable obser- 
vation of meteors and auroras ; for as late as 1790 the 
' Decade philosophique,' as well as the Paris Academy and 
many learned persons, ridiculed the authentic reports of 
the fall of meteors, and Chladni's classical dissertation on 
the stone of Pallas.^ It seems as if the purest love of 


^ W^hen in the year 1790 the 
municipality of Juillac in Gascony 
submitted a report, signed by more 
than 300 eyewitnesses, to the Paris 
Academy, on a fall of stones which 
had there taken place, one of the 
editors of the 'Decade philoso- 
phique ' remarked that it would be 

better to deny such incredible things 
than to enter into any explanations. 
Bertholon could not help pitying a 
community which had such a foolish 
Tiiaire, and remarked in the * Jour- 
nal des Sciences utiles ' : " How sad 
it is to find a whole municipality 
attesting formally by protocol popu- 




17. nature, the greatest devotion of the observer and the 
encyofmere collector, lead onlv a little way in finding out the hidden 

observation. ./ o 

paths of natural things or the behaviour of natural ob- 
jects ; and however grateful we must be to those pioneers 
of knowledge who with unrewarded patience amass the 
material for later theorists, it is to the classification of a 
Linnaeus, to the arrangements of a Cuvier, to the theories 
of a Darwin, to the measurements of a Bradley and a 
Herschel, most of all to the formulae of a Newton or a 
Gauss, followed by the calculations of their pupils, that 
we are indebted for a real grasp, for a comprehensive 
knowledge, of great masses of natural phenomena. 

Next to the pure love of nature, the desire to apply 
natural knowledge, and to make it useful for practical 
purposes, has rendered in return great services to science. 
The Koyal Society and the Royal Institution had both 
from their infancy a large admixture of the practical 
spirit. These were founded, more even than the academies 
abroad, to a great extent upon the desire to make know- 
ledge useful. 

The Governments of England and of France promoted 


lar fables which are only to be pitied ! 
What can I add to such a protocol ? 
The philosophical reader will him- 
self suggest what to say when he 
reads this authentic proof of an 
evidently wrong fact, of a pheno- 
menon which is physically impos- 
sible" (Wolf, 'Geschichte der Astro- 
nomie,' 1877, p. 697 sq.) Chladni 
published his essay on the large 
mass of iron found by the traveller 
Pallas in Siberia in the year 1794, 
and, in spite of adverse criticisms, 
followed it up by a catalogue and 
an atlas of meteoric stones, sug- 
gesting that they were of cosmic 

origin. Fortunately, a remarkable 
fall of stones, accompanied by 
meteoric phenomena, took place in 
1803 not far from Paris, at I'Aigle 
in the department de I'Orne, and 
Biot was commissioned by the 
Academy to proceed to the dis- 
trict and examine the case. In the 
* Relation,' &c., which he read before 
the Institute, he established the 
fact that a meteor exploded in the 
district, and that at the same time 
a fall of many thousand stones, 
weighing about 20 tons, took place 
(Biot, 'Melanges scientifiques et 
litt^raires,' vol. i. p. 15 sqq.) 

the study of the " mechanics of the heavens " by offering 
large prizes for scientific and practical means of deter- 
mining the longitude at sea. The lunar theory, which 
has occupied the attention of the greatest mathematicians 
since Newton — of Euler, Clairaut, and Tobias Mayer in 
the last century ; of Burckhardt, Plana, and Hansen, of 
Delaunay and Adams, in the present century — was an 
outcome of this. It still engages the attention of scien- 
tific minds, involving as it does all the most delicate 
astronomical calculations, whilst for practical nautical 
purposes the moon has ceased to be the great timekeeper, 
and has since 1763 been replaced by the wonderful 
chronometers of Harrison and his successors. A similar 
stimulus both to abstract scientific research and to the 
perfection of the practical instruments of measurement 
was given in this century by the development of sub- 
marine telegraphy : in this case both sides of the problem, 
the scientific and the practical, were attacked, and carried 
to a high degree of perfection by one and the same mind^ — 


^ William Thomson's (Lord Kel- 
vin's) investigations and inventions, 
which made submarine telegraphy 
at long distances commercially prac- 
ticable, refer mainly to the over- 
coming of the "embarrassment" 
occasioned by the property (dis- 
covered by Werner Siemens, 1849, 
and investigated by Faraday, 1854) 
which submerged cables possess 
of "retaining a quantity of elec- 
tricity in charge along the whole 
surface." In 1854 Thomson made 
a full theoretical examination of 
this phenomenon, showed how it 
depended on the length, the elec- 
tric resistance, and the electro- 
static capacity of the line, and gave 
a mathematical formula, with prac- 
tical examples of the retardation of 

I the signals and the gradual increase 
I of the strength of the electric cur- 
\ rent at the receiving end of long 
submarine cables (" On the Theory 
of the Electric Telegraph" and 
other papers, reprinted in the 2nd 
vol. of 'Math, and Phys. Papers,' 
1884). The importance of con- 
structing delicate instruments for 
registering feeble signals, and of 
a method for reducing the time 
of single signals, became evident 
through these theoretical investi- 
gations. The mirror galvanometer 
was first used in 1858 on the first 
Atlantic cable, and afterwards on 
the successful cables of 1865 and 
1866. It was followed by the 
spark -recorder, which led to the 
syphon -recorder (1867-70), which 



an almost unique instance of the combination of abstract 
reasoning and practical inventiveness. An almost equally 
important problem, having both scientific and practical 
interest, arising out of the Newtonian gravitation formula, 
is the problem of the tides. Here also the first suggestions 
towards a theory were given in the * Principia,* whereas 
the first attempt at a solution is contained in Laplace's 
great work. A closer approximation was reached by Sir 
W. Thomson in his extensive theoretical and practical use 
of Fourier's mathematics. 

I shall have frequent opportunity to refer to the bene- 
ficial and fructifying influence which practical problems 
have exerted on scientific thought ; ^ in fact, in spite of 

has since been in use in submarine 
telegraphy. The best account of 
these discoveries and inventions is 
to be found in Lord Kelvin's own 
papers, a good summary being given 
in his short article in Nichol's 
•Cyclopedia,' reprinted as No. 82, 
vol. ii. p. 138. 

^ How much science owes to the 
practical interests of navigation can 
be seen by a glance at the subjects 
contained in the third volume of 
Lord Kelvin's * Popular Lectures 
and Addresses.' The Tides, Deep- 
Sea Sounding, Cable-Laying, and 
Terrestrial Magnetism all furnish 
important practical as well as high- 
ly abstract theoretical problems, 
the solution of which demands new 
instruments and new methods of 
calculation. The phenomena of 
the tides and those of terrestrial 
magnetism are intimately connect- 
ed with two of the most refined 
mathematical theories which this 
century has developed. The for- 
mer was first attacked by the so- 
called equilibrium theory — the pro- 
blem being to find the figure of 
equilibrium of a rotating ellipsoid 

covered with water under the in- 
fluence of various attracting forces. 
Laplace, followed by Airy and 
Thomson, showed how it is much 
more a question of dynamics than 
of statics, and that it resolves itself 
into the analj'sis and subsequent 
synthesis of a number of periodic 
movements, dependent upon the 
several periodic changes of the ro- 
tation of the earth and the revo- 
lutions of the moon round the 
earth and the sun. A general 
method of dealing mathematically 
with the superposition of several 
periodic changes had been invented 
by Fourier in the early part of this 
century, and it was this which, 
especially in the hands of Lord 
Kelvin and his brother — the late 
Prof. James Thomson — led to the 
harmonic analysis of tide motion 
and the subsequent invention of 
tide-predicting apparatus (see the 
above volume, p. 177 sqq.) The 
observation of the magnetism of 
the earth is connected with great 
improvements in the theory and 
construction of the mariner's com- 
pass, suggested and carried out by 


the great reciprocal influence which science has gained in 
the course of this century over practical life, I am still 
doubtful whether scientific thought has, at the end of 
our century, as yet balanced the debt which it owes to 
practical inventors. It is instructive, for instance, to 
consider how much, in the hands of Eumford, of Sadi 
Carnot, of Him, and of Eankine, science has learnt from 
the steam-engine, and to reflect whether from all the 
theoretical insight gained any really radical improve- 
ment of the steam-engine — still ouq of the most imperfect 
machines — has resulted.^ 

Lord Kelvin ; and it has in an- 
other direction led to remarkable 
scientific results in the hands of 
Gauss, who between the years 1830 
and 1840 brought the theory al- 
most to perfection. Here again 
the physical phenomenon required 
for its treatment a special mathe- 
matical analysis, which Gauss great- 
ly furthered in his ' Allgemeine 
Lehrsiitze in Beziehung auf die im 
verkehrteu Verhiiltnisse des Quad- 
rats der Entfernung wirkenden 
Anziehungs- und Abstossungs- 
Krafte ' (1840). This is a mathema- 
tical investigation of the Newtonian 
gravitation-formula. Gauss followed 
out the theories of Laplace and La- 
grange simultaneously with Green, 
whose now celebrated memoir on 
the subject remained long unknown 
(see supra, pp. 231, 247). The ma- 
thematical theory showed that in a 
sphere containing a certain amount 
of attracting (magnetic) matter an 
ideal distribution on the surface of 
the sphere can be found which 
takes the place of the real but un- 
known distribution in the interior, 
and that if through observation the 
necessary data are supplied, the 
magnetic condition of any point 
on the surface can be foretold with 
great approximation. As an ex- 

ample. Gauss foretold from the 
imperfect data at his command 
the position of the south magnetic 
pole. In 1840 Capt. Sir James Ross 
approached it sufiiciently to show 
the correctness of the calculation. 
The theoretical investigations in 
connection with magnetic attrac- 
tion and with tidal movements 
have remodelled the methods of ob- 
servation of the phenomena them- 
selves, the older methods having 
proved to be in many ways insuf- 
ficient. A full account of Gauss's 
labours here referred to will be 
found in E. Schering, * C. F. Gauss 
und die Erforschung des Erdmag- 
netismus,' Gottingen, 1887. 

^ I refer in this matter to two 
addresses delivered recently — one 
by Prof. Unwin ('Electrician,' vol. 
35, pp. 50 and 79) on ''The De- 
velopment of the Experimental 
Study of Heat - Engines " ; the 
other by Prof. Lodge on "The 
Second Law of Thermodynamics " 
('Electrician,' vol. 35, p. 80 sqq.) 
From a perusal of these papers one 
gains the impression that science 
has been more successful in teach- 
ing us why the steam-engine is so 
wasteful a machine than in show- 
ing how it can be greatly improved. 
It is interesting to hear that "al- 


■' f 




19. The mathematical formula is the point through which 

effect of all the light gained by science passes in order to be of 
cai formula, ^jgg ^q practice ; it is also the point in which all know- 
ledge gained by practice, experiment, and observation must 
be concentrated before it can be scientifically grasped. 
The more distinct and marked the point, the more con- 
centrated will be the light coming from it, the more un- 
mistakable the insight conveyed. All scientific thought, 
from the simple gravitation formula of Newton, through 
the more complicated formulae of physics and of chem- 
istry, the vaguer so-called laws of organic and animated 
nature, down to the uncertain statements of psychology 
and the data of our social and historical knowledge, alike 
partakes of this characteristic, that it is an attempt to 
gather up the scattered rays of light, the diffused know- 
ledge, in a focus, from whence it can be again spread out 
and analysed, according to the abstract processes of the 
thinking mind. But only where this can be done with 
mathematical precision and accuracy is the image sharp 
and well defined, and the deductions clear and unmis- 
takable. As we descend from the mechanical, through 
the physical, chemical, and biological, to the mental, 
moral, and social sciences, the process of focalisation 
becomes less and less perfect, — the sharp point, the 

most all the present difference be- 
tween the best steam-engine and 
the worst is some 5 or 6 per cent " 
(Lodge). Prof. Unwin sums up by 
saying: "Since 1845 purely scien- 
tific men, scientific experimenters, 
and practical engineers have all 
been engaged in the study of the 
steam-engine. I do not believe 
that any one of the three can 
claim all the credit for the im- 

provement of the steam-engine to 
the exclusion of either of the 
others. . . . Representing perhaps 
rather the scientific than the prac- 
tical interest, I do not think that 
the mathematical and physical re- 
searches of which I have tried to 
give an account have had no in- 
fluence on the practical business of 
the engineer." 


focus, is replaced by a larger or a smaller circle, the 
contours of the image become less and less distinct, 
and with the possible light which we gain there is 
mingled much darkness, the source of many mistakes 
and errors. But the tendency of all scientific thought 
is towards clearer and clearer definition ; it lies in the 
direction of a more and more extensive use of mathe- 
matical measurements, of mathematical formulae. 

There is probably no science which has come so per- 
fectly under the control of this kind of mathematical ex- 
pression as has astronomy since the time of Newton or of 
Laplace, and, we may add, there exists probably no mathe- 
matical formula which has stood the test of application to 
existing phenomena so long and so thoroughly as the 
gravitation formula of Newton. It possesses two unique 
properties which no other formula possesses — so far as we 
can now see — it is universal ^ and it is accurate.^ These 

^ The law of gravitation can be 
called the first and most general 
physical law or statement of uni- 
versal application. The laws of 
motion may be called mechanical 
or dynamical statements. Both 
the law of gravitation and the 
laws of motion describe facts, and 
have been found by experience ; 
but the laws of motion con- 
tain no physical constant— i.e., 
no quantity which requires to be 
fixed and measured by observa- 
tion, and the absolute value of 
which has for us at present no 
ulterior meaning. The law of gra- 
vitation has one physical constant, 
the universal gravitation constant 
(see p. 320). As it measures what 
we call matter, it need not be de- 
termined, and its actual determin- 
ation, which has been accurately 
made only in recent times, has not 

in any direction advanced our gen- 
eral physical knowledge. For all 
practical purposes of physics the 
unit of mass is a weight, just as for 
all commercial purposes gold is the 
standard of value. The astrono- 
mical view permits us to go a step 
further and express the mass of a 
pound of matter in units of time 
and space, and the political econo- 
mist may seek for a real standard 
of value — for instance, an article 
of food like wheat. Other funda- 
mental physical laws or general 
statements involve other physical 
constants, as we shall see later on. 
2 The accuracy of the so-called 
laws of nature, or, more correctly, 
of the expressions which science 
gives to the laws of nature, is a 
very important question. Little is 
said on this point in the ordinary 
text -books. It is only in verj' 





two properties of the gravitation formula have been brought 
out by a long line of investigations, carried on with the 
view of substantiating or of refuting the formula. They 
mark the development of whole sciences, the foundation 
of quite novel branches of research. I propose briefly to 
follow up these developments. 
MatteJ'and Common-scnse has never had any difficulty in knowing 
ScSfy^"' ^^^^ matter and force are, or in defining them for the 
defined. purposcs of practical life. But it took thousands of years 
to find a definition of these quantities which could serve 
as the basis of exact measurement, and permit calcula- 
tions of results into which both factors entered in varying 

recent publications that attention 
is sufficiently drawn to the fact 
that very few mathematical for- 
mulae in physics or chemistry are 
-more than approximations. The 
law of gravitation is one of the few 
mathematical expressions which, 
besides being universal, have stood 
the most rigorous tests as to accur- 
acy. A most interesting attempt 
to prove the inaccuracy of New- 
ton's law was made, but speedily 
abandoned, by Clairaut, one of 
the earliest Newtonians in the old 
Academy of Sciences. Clairaut 
began about 1743 to study the 
lunar theory in the light of New- 
ton's system, which Madrin be- 
fore him had already despaired 
of reconciling with the facts of 
observation. When he himself, 
on calculating the annual motion 
of the moon's apogee (or farthest 
point in its orbit round the 
earth), found only half the value 
which observation furnished, he was 
tempted in his communication to 
the Academy of November 1 747 to 
suggest that the Newtonian for- 
mula might require a correction for 
great distances. This suggestion 
was followed, as Lalande tells us, 

by a veritable scandal in the learned 
world. Buffon, for purely meta- 
physical reasons, objected to this 
infringement of the simplicity of 
the laws of the universe. The 
opponents of Newton's system had 
a short triumph, which however 
was speedily reversed when Clair- 
aut, putting a greater precision 
into his calculations by taking 
inequalities into account which he 
had previously neglected, explained 
to the Academy in May 1749 that 
he had succeeded in reconciling the 
movement of the moon's apogee 
with the law of attraction accord- 
ing to the inverse square of the 
distance. From that time the 
Newtonian theory, to which only 
shortly before mathematicians like 
Euler had been won over, reigned 
supreme. See Lalande in the 4th 
volume of Montucla's ' Histoire 
des Mathematiques,' p. 67, &c. 
Euler's merits in solving many 
problems in physical astronomy were 
so great that the Academy procur- 
ed permission from Louis XV. to 
receive him as a surnum&aire, the 
eight places granted to external 
members being all occupied. 

quantities and in varying combinations. That a smaller 
quantity of matter in motion could produce the same 
action as a larger which was moving slowly, or even 
apparently at rest, and acted only by what is termed its 
dead-weight, was a well-known phenomenon ; but it was 
only within the half-century which preceded the publica- 
tion of the ' Principia ' that, through the labours of Galileo 
and of Huygens, mathematical definitions and simple 
formulae were laid down, and generally accepted, which 
gave the means of accurately measuring and calculating 
the phenomena of moving bodies and the combination of 
forces. These labours resulted in a definition of matter 
which, translated into the language of our day, says that 
matter is that which moves and is capable of resisting 
any change of motion. ( Motion is a measurable quan- 
tity. For its measurement we require the measurement 
of space and time, and the well-known relation of both 
— viz. J velocity. ) 

The above formula therefore says that matter is mea- 
sured by the resistance it offers to change of motion or 
of velocity. And correspondingly force is that which is 
capable of producing change of motion, or velocity in 
matter, and it is measured by the amount of change it 
produces. Given a definite, though unknown, force, 
portions of matter — i.e., masses — can be compared by the 
resistance they offer to the change of their motion ; the 
smaller the change the larger the mass or quantity of 
matter. Given a definite, though unknown, quantity of 
matter, forces can be measured by the different changes 
they produce in the motion — i.e., the velocity — of this 
quantity ; they are greater or smaller in the proportion 





Weight and 

of the change of velocity which they produce. One of 
the great difficulties which stood in the way of the fixing 
of these very simple mathematical relations and defin- 
itions was the fact that all matter with which we can 
experiment is under the influence of a constant but un- 
known force, that which makes it fall if not supported. 
It was only by freeing themselves from the effect of this 
constant force, or by balancing it, that philosophers 
gradually arrived at the conception and definition of 
mass, or quantity of matter, as something independent 
of its weight. It was reserved for Newton to show and 
define the exact relation which weight bears to the other 
properties of matter defined and measured by his pre- 
decessors. By doing so he added a new definition, a new 
means of measuring the quantity of matter or its mass, 
showing at the same time to what extent the popular 
measure of matter — i.e., its weight — could be accurately 
used for scientific purposes. Again, to express it in the 
language of our day, Newton showed that matter is not 
only that which offers resistance to change of motion, 
but also that which causes change of motion in other 
portions of matter: it is not only the object on which 
force spends itself, it is the seat of this force, and the 
degree in which it can change motion in other portions 
of matter is proportional to the degree in which it 
resists the change of its own motion — in other words, 
the gravity or weight of matter is proportional to its mass 
or inertia, and is not dependent on any other difference, 
whether of size or of quality. This second universal 
property of matter, which brought out more clearly the 
reciprocity of all mechanical, and subsequently of all 

physical actions, is, however, dependent on the mutual 
distances of the particles of matter, and can therefore be 
altered, but can as little as the existence of matter itself 
be removed. This view of Newton's explained or de- 
scribed clearly^ the phenomena of moving and falling 

^ The distinction between an ex- 
planation and a description of the 
facts of nature has been slowly de- 
veloped in the course of modern 
thought. Probably Leibniz was 
the first to insist on it, and to 
maintain in the abstract that all 
description of nature w^ould be me- 
chanical, but that the explanation 
or interpretation of nature must be 
spiritual. But the first practical 
instance of this important distinc- 
tion is really to be found in New- 
ton's philosophy. In many pas- 
sages of the ' Principia,' and especi- 
ally in the * Optics,' the double view 
of the problems of philosophy is 
clearly indicated. The principles 
of science since the time of Newton 
are general facts, established by 
experience and put into mathe- 
matical language, admitting of con- 
stant verification by observation 
and by the deductions of the cal- 
culus. These principles are not 
the ultimate causes, but only a 
concise description of some of the 
phenomena of nature. These prin- 
ciples Newton calls mathematical — 
referring to measurable quantities 
— and distinguishes them from the 
philosophical principles! ('Princ.,' 
Ist ed,, p. 401). Especially as re- 
gards gravitation, Newton explains 
many times that he uses this term 
not as an explanation, but only as 
a mathematical description of the 
force with which bodies approach 
each other, whatever the cause of 
this phenomenon may be, which he 
leaves others (called with some 
irony metaphysicians) to deter- 
mine ('Optics,' query 31). That 


Newton, besides giving the precise 
mathematical principles of all future 
dynamical science, indulged also in 
further speculations, which he put 
into the form of queries and ad- 
vanced with hesitation and merely 
tentatively, gave his opponents 
ample opportunity to attack the 
doubtful and uncertain statements 
in his philosophy. Instead of 
studying and understanding the 
mathematical truths of the 'Prin- 
cipia,' they attacked the doctrines 
which were fragmentarily put for- 
ward in the queries to the ' Optics ' 
or added in the general scholium 
at the end of the second edition of 
the 'Principia.' Roger Cotes in 
his preface to the second edition 
of the 'Principia,' and Clarke in 
his correspondence with Leibniz, 
pointed out the difference between 
Newton's descriptive and calculat- 
ing and the older or metaphysical 
philosophy. They were, however, 
more interested in disproving the 
atheistical consequences of which 
Newton's philosophy had been ac- 
cused than in clearly insisting on 
the fundamental difference between 
mathematical and metaphysical 
principles — i.e., between the exact 
and the philosophical views of na- 
ture. And in Bentley's Boyle lec- 
tures, delivered in 1692 and 1693, 
the principles of Newton's philos- 
ophy were specially brought for- 
ward to refute atheism, an under- 
taking which Newton himself sup- 
ported in his contemporary corre- 
spondence with Bentley, published 
half a century later, in 1756. 

i ? 




masses, not only at a point on the surface of our earth, 
where the force of gravity can be considered to be con- 
stant, but all through the universe, where it varies with 
the distances of the moving masses. 

The Newtonian formula of gravitation was not at once 
accepted by philosophers as a correct statement of the 

ultimate r ^ r r 

property of facts of nature. It appeared to limit the existence of 

matter. *■ •*■ 


not an 

^ The philosophy of Descartes, 
which then reigned on the Con- 
tinent, seemed in many ways to 
hinder the acceptance of Newton's 
doctrines. Descartes had taken a 
great step in advance in philosophi- 
cal teaching ; he had placed mathe- 
matics at the head of his doctrine ; 
he had opposed the older metaphy- 
sical methods, and he had, through 
his application of algebra to geo- 
metry, made great progress towards 
a mechanical description of phe- 
nomena. But he had not separated 
the description from the interpre- 
tation of nature. Philosophy and 
science remained united, the mathe- 
matical formulsc were only a new 
kind of metaphysics, incapable with- 
out observation of making any real 
advance in the knowledge of nature. 
The facts of geometry which are 
required for an application of an- 
alysis are the well-known axioms of 
Euclid. An application of analysis 
to dynamics requires a knowledge 
of the laws or fundamental proper- 
ties of motion. These were not 
correctly and completely known to 
Descartes ; Newton placed them at 
the head of his mathematical phil- 
osophy of nature. A further appli- 
cation to physical phenomena re- 
quired a knowledge of some general 
physical fact : such was supplied by 
Newton in the gravitation formula. 
The laws of motion and gravitation 
once admitted as facts, there was 
plenty to do for mathematics. Not 
so with Descartes. In his philoso- 

phy the basis of facts was too nar- 
row and indefinite, and had to be 
supplemented by metaphysical sup- 
positions and deductions. The field 
for mathematical reasoning not be- 
ing sufficiently prepared and wide 
enough, Descartes had speedily got 
back again into metaphysical rea- 
soning. In fact the doctrines of 
Newton, in which mathematical and 
philosophical deductions had for the 
first time been successfully separ- 
ated, encountered on the Continent 
the doctrines of Descartes, in which 
mathematical and philosophical de- 
ductions were hopelessly mixed up. 
On one point e.specially the two 
views seemed to clash. Descartes 
had by metaphysical considerations 
tried to define what matter is. 
Newton had postponed the answer 
to this question, but had defined 
mathematically two properties of 
matter — viz., inertia and gravita- 
tion. Descartes' metaphysical con- 
siderations had led to the concep- 
tion that matter and extension were 
identical, that space therefore could 
not be empty. Newton, occupying 
himself not with matter in the ab- 
stract, but only with moving observ- 
able matter, had established the 
general law of gravitation, leaving 
it undecided whether the apparent 
vacuum existing between visible 
bodies was really empty or full. 
For the deductions from the law 
of gravitation it might in the 
first instance be considered empty. 
Thus on this question about space 

matter to certain changing places in an empty space, 
and to attach the forces of nature likewise to this dis- 
tribution of matter. This was hardly the intention of 
the author himself, who saw in the so-called law of 
gravitation not a final explanation, but only a descrip- 
tion of the phenomena of nature — notably of the larger 
phenomena. That behind the mathematical formula there 
may be conditions which are capable of further analysis, 
— that the larger or molar phenomena of moving bodies 
are made up of their smaller or molecular movements, 
was well known to Newton. For before he approached 
the great laws of the universe he had been occupied 
with investigations which led him into the minutest 
phenomena, those of light and colour. To him, indeed, 
are owing some of the observations and methods by 
which subsequently the greatest and the smallest meas- 
urements of natural objects have been carried out. But 
in exact science the deeper philosophical meanings dis- 
appear where the strict mathematical deductions point 
to definite conceptions, mark certain fixed paths of 
research, and promise definite results. The eighteenth 
century gradually settled down to a wholesale adoption 
of the gravitation theory — looked upon space as empty, 
upon matter as subject to a definite though changing 
distribution in space, and upon the forces of nature as 
attached to certain moving centres, between which only 
a mathematical, but no intelligible physical, connection 

— whether it was empty or full — 
the two doctrines came into conflict. 
That Newton's position was not a 
final, but only a provisional one, 
was overlooked ; he was accused of 
introducing again the occult quali- 

ties of the scholastic philosophy, and 
a great fight was started against his 
views in the Academy of Sciences, 
where Descartes' philosophy reigned 





could be traced.^ What to some contemporaries of Newton, 
and even to Newton himself, seemed an absurdity — that 
action could take place at a distance ^ — became through 

^ Voltaire, who did not dive very 
deep into the teachings of Newton, 
gives a graphic description of the 
different opinions then current in 
English and French learned circles. 
In his 'Lettres sur les Anglais,' 
written about the time of the death 
of Newton, after having discoursed 
on Quakerism, the Church and 
Government, on vaccination, Bacon 
and Locke, he devotes four chapters 
to the philosophy of Newton, which 
he contrasts with that of Descartes. 
* ' Un Frangais qui arrive Ji Londres 
trouve les choses bieu changes en 
philosophie, comme dans tout le 
reste. II a laisse le monde plein, il 
le trouve vide. Paris on voit 

I'univers compose de tourbillons de 
matiere subtile, a Londres on ne 
voit rien de cela. Chez nous c'est 
la pression de la lune qui cause le 
flux de la mer ; chez les Anglais 
c'est la mer qui gravite vers la 
lune. . . . Chez vos Cartesiens 
tout se fait par une impulsion qu'on 
ne comprend guere ; chez M. New- 
ton c'est par une attraction dont on 
ne connait pas mieux la cause. . . . 
Descartes assure encore que I'^ten- 
due seule fait la matiere, Newton y 
ajoute la solidite" (lettre xiv.) 

2 " You sometimes speak of grav- 
ity as essential and inherent to 
matter. Pray, do not ascribe that 
notion to me ; for the cause of grav- 
ity is what I do not pretend to 
know" (Newton's 2nd letter to Bent- 
ley, 17th Januarj' 1692-93). " It is 
inconceivable that inanimate brute 
matter should, without the media- 
tion of something else, which is not 
material, operate upon and affect 
other matter without mutual con- 
tact, as it must be, if gravitation, 
in the sense of Epicurus, be essential 
and inherent in it. And this is one 

reason why I desired you would not 
ascribe innate gravity to me. That 
gravity should be innate, inherent, 
and essential to matter, so that one 
body may act upon another at a 
distance through a vacuum, without 
the mediation of anything else, by 
and through which their action and 
force may be conveyed from one to 
another, is to me so great an ab- 
surdity that I believe no man, who 
has in philosophical matters a com- 
petent faculty of thinking, can ever 
fall into it. Gravity must be caused 
by an agent acting constantly ac- 
cording to certain laws; but whether 
this agent be material or immaterial, 
I have left to the consideration of 
my readers " (3rd letter to Bentley, 
5th February 1692-93). And in 
the fifth answer to Leibniz (pub- 
lished after Leibniz's death) Clarke 
says: *'That the sun attracts the 
earth . . . — that is, that the earth 
and sui^ gravitate towards each 
other, or tend towards each other, 
with a force which is in a direct 
proportion of their masses, . . . 
and in an inverse duplicate propor- 
tion of their distances, and that the 
space betwixt them is void — that is, 
has nothing in it which sensibly re- 
sists the motion of bodies passing 
transversely through : all this is 
nothing but a phenomenon or actual 
matter of fact, found by experience. 
That this phenomenon is not pro- 
duced sans moyen — that is, without 
some cause capable of producing 
such an effect — is undoubtedly true. 
Philosophers therefore may search 
after and discover that cause, if 
they can ; be it mechanical or not 
mechanical. . . . The phenomenon 
itself, the attraction, gravitation, or 
tendency of bodies towards each 
other, and the laws or proportions 

a century of confirming thought, observation, and calcula- 
tion an adopted axiom, and the accepted formula of all 
physical explanations. For a time, indeed, the exact 
formula of gravitation seemed liable to some correction, 
but gradually the apparent anomalies disappeared, and 
even in our century none of the many attempts to modify 
the gravitation formula, to look upon it as merely an ap- 
proximation, or to go behind it and find some more general 
relation from which it could be deduced, have been gen- 
erally useful or acceptable.^ It still stands there as the 
only universally accepted mathematical expression which 
corresponds to a general physical property of natural 

Two different lines of thought combined to give the 
formula of Newton a still wider importance than its 
author primarily intended, or than it has been found 
possible to maintain in the course of further inquiry. The 
first was the ancient philosophical idea of attraction, which, 
without being mathematically defined and practically use- 
ful, had nevertheless, from the dawn of Greek speculation 

of that tendency, are now suffici- 
ently known by observations and 
experiments. If this or any other 
learned author can by the laws of 
mechanism explain these phenom- 
ena, he will not only not be con- 
tradicted, but will, moreover, have 
the abundant thanks of the learned 
world. But in the meantime, to 
compare gravitation, which is a phe- 
nomenon or actual matter of fact, 
with Epicurus' declination of atoms 
seems to be a very extraordinary 
method of reasoning" (§§ 118-124, 
Leibniz's * Philosophische Schrif- 
ten,' by Gerhardt, Berlin, 1890, vol. 
vii. p. 439 sq. ) 
^ A very complete account of 

these different attempts will be 
found in the writings of C. Isen- 
krahe, *Das Riithsel von der 
Schwerkraft,' Braunschweig, 1879 ; 
"Euler's Theorie von der Ursache 
der Gravitation," in ' Zeitschrif t f iir 
Mathematik und Physik,' vol. xxvi. ; 
'Ueber die Fernkraft,' Leipzig, 
1889; "Ueber die Zuriickfiihrung 
der Schwere auf Absorption," in 
' Abhandlungen zur Geschichte der 
Mathematik,' vol. vi., Leipzig, Teub- 
ner, 1892. See also as bearing on 
this subject, Paul du Bois-Reymond, 
' Ueber die Grundlagen derErkennt- 
niss in den exacten Wissenschaft- 
en,' Tiibingen, 1890. 






and repul- 

and all through ancient and medi?eval philosophy, figured 
as one of the occult causes or forces which regulate the 
behaviour of living and dead matter. That the force of 
attraction alone would result in an accumulation of all 
matter in one body was of course recognised, and a second 
arbitrary and occult force — that of repulsion — was intro- 
duced as a counteracting or balancing agent. 

In Newton's system of the universe the balancing force 
was found to be that of an inherent initial motion which 
matter, in consequence of its mass or inertia, maintained 
in addition to the motion due to gravitation. If motion 
and inertia were able to account for the apparent repul- 
sion of bodies at a distance, it might be that they could 
also account for their apparent attraction. This idea, 
though expressed about the time when the Newtonian 
gravitation formula was established, did not meet with 
serious attention till far on in our century other lines of 
thought led to similar views.^ The phenomena of attrac- 

^ Newton himself seems to have 
looked for a mechanical explanation 
of gravitation. Long before the 
publication of the 'Principia' he 
laid before the Royal Society a 
paper containing "a hypothesis 
explaining the properties of light " 
by the assumption of an "eetherial 
medium, much of the same consti- 
tution with air, but far rarer, 
subtiler, and more strongly elastic " 
(Letter to Oldenburg, January 25, 
1675-76, given in Brewster's 'Me- 
moirs of Sir I. Newton,' vol. i. 
p. 390 sqq.), which might explain 
magnetic and, electric phenomena, 
as well as those of gravitation, and 
especially light. And in a letter 
to Robert Boyle, of 28th February 
1678-79 (Brewster, vol. i. p. 409), 
he reverts to this subject. Having, 

however, in the course of the next 
decade found it more useful to work 
out the mathematical conclusions 
to be drawn from the phenomenon 
of gravitation, which was a fact and 
not a hypothesis, he abandoned the 
metaphysical part of the subject, 
the question how gravitation was 
to be explained, " finding" (as Mac- 
laurin says in his account of New- 
ton's discoveries) " that he was not 
able, from experiment and obser- 
vation, to give a satisfactory ac- 
count of this medium and the 
manner of its operation in produc- 
ing the chief phenomena of nature." 
And in his letter to Boyle, as well 
as in a later one to Halley (20th 
June 1886, Brewster, vol. i. p. 439), 
he carefully distinguishes between 
the results of the 'Principia' and 



tion and repulsion at a distance rather received additional 
weight and importance when, following Newton's cosmical 
measurements. Cavendish and Coulomb, towards the end 

the mere framing of hypotheses 
and conjectures, for which he pro- 
fesses to have little fancy, though 
" the heads of some great virtuosos 
run much upon hypotheses"; and 
he describes his earlier speculations 
as "guesses which I did not rely 
on." In fact, the elaboration of 
the theorems contained in the 
* Principia ' marks the transition 
from the metaphysical to the exact 
or scientific treatment of natural 
phenomena. Before Newton showed 
the far-reaching consequences, the 
unexpected grasp of a simple mathe- 
matical formula in combining facts 
apparently disconnected, no one 
could have suspected that such 
would be possible, and it is not to 
be wondered at that when once 
philosophers realised the power of 
such formula}, an opposite move- 
ment set in through which mathe- 
matical processes were extolled at 
the expense of experiment and 
observation on the one side, and 
of philosophical reasoning on the 
other. Newton himself never fell 
into this error. He knew well the 
importance of observation, and he 
retained to the end of his life a 
gi-eat interest in the philosophical 
or metaphysical problems which lay 
beyond or behind the mathemati- 
cal statement ; he carefully distin- 
guished between the vis gravitatis 
and the causa gravitatis. Two other 
great thinkers, second only to New- 
ton himself, took up a similar posi- 
tion to the law of gravitation. 
"Whilst firmly believing in it, they 
considered it to be not an ultimate 
law of nature, a causa occulta, but 
believed that it must be possible to 
derive it from some mechanical 
properties of matter. The one was 
older than Newton. It was Huy- 

gens (1629-95) who through his 
analysis of centrifugal forces (1673) 
had done so much to pave the way 
for Newton's own work. In 1690, 
after having paid a visit to England 
in order to become more intimately 
acquainted with Newton's work, he 
published at Leyden his 'Discours 
sur la Cause de la Pesanteur,' a 
treatise which was little noticed at 
the time, and in which he is sup- 
posed to have revived the vortices 
of Descartes. Those who have care- 
fully examined it (Fritsch, ' Theorie 
der Newton'schen Gravitation,' &c., 
Konigsberg, 1874 ; and Isenkrahe, 
' Das Riithsel von der Schwerkraft,* 
p. 87, &c.), find that Huygens re- 
verted to his conception of a mate- 
rial fluid, an ether, such as he had 
suggested for the explanation of 
optical phenomena, "which sur- 
rounds the earth up to very great 
distances, which consists of the 
minutest particles, which fly about 
in the most different ways in all 
directions with tearing velocity " — 
an anticipation surely of Lesage's 
"ultramundane corpuscles." The 
other great thinker who, whilst 
firmly believing in Newton's law, 
sought for a mechanical explanation 
of it, was Leonhard Euler (1707-83). 
In his ether theory, to which he 
reverts frequently, he made an 
attempt to explain the various 
physical agencies, among them 
gravitation (1743, in his 'Disser- 
tatio de Magnete,' which received 
in 1744 the prize offered by the 
Paris Academy), by the pressure of 
the ether. He admits the difficulty 
of the problem, but insists upon the 
necessity of finding a mechanical 
cause for gravitation. See Isen- 
krahe in 'Zeitschrift fiir Mathe- 
matik und Physik,' vol. xxvi. ; but 





and mag- 
netic action 

of the last century, subjected the less universal terrestrial 
phenomena of magnetic and electric action to exact mea- 
surements, finding that a formula corresponding to the 
gravitation formula described them with surprising ac- 
curacy, with this remarkable difference, that here not only 
attractive but also repulsive forces, following the same 
mathematical relations as to mass and distance, came into 
play. To these confirmatory discoveries must be added 
the measurement of the intensity of radiations which 
proceed from centres, such as those of light and heat, 
made by various philosophers during the latter half of 
the last century. Newton, and his great successor La- 
place more than a century after him, both favoured the 
emission or emanation hypothesis of light, and it was 
thus natural to fasten upon the analogy which existed 
between the intensity in which radiation, gravitation, and 
electric and magnetic action change with the distance 
from their respective centres. All these agencies came 
emanations, thus uudcr the general conception of forces emanating 
from fixed centres, and spreading through space, in the 
proportion of the superficial area of the spheres described 
around their centres with increasing radii — i.e., decreasing 
or becoming diluted in the ratio of the squares of these 
radii or distances. These analogies were indeed recognised 
to be very imperfect, inasmuch as light and radiant heat 
occupy a measurable time to spread from their centres, 
whereas the time occupied by the force of gravitation is 

Law of 

especially Miething, *L. Euler's 
Lehre vom Aether,' Berlin, 1894. 
In the course of this century the 
mechanical theory of gravitation, 
including the attempts of Lesage, 
Euler, Huygens, and Newton him- 

self, has again received attention 
through Faraday's, Maxwell's, and 
Hertz's electric theories, and Wm. 
Thomson (Lord Kelvin) has especi- 
ally studied the ideas of Lesage. 
Of this more later on. 

either exceedingly small or this force is propagated 
instantaneously through the greatest cosmical distances 
which come under our notice. Then, again, light and 
radiated heat spend themselves as they meet with reflect- 
ing or absorbing bodies, whereas gravitation does not 
seem to be affected by intervening or screening bodies.^ 

^ It is now known that this 
screening effect exists likewise in 
magnetic and electric action. In 
the formula which expresses the 
action at a distance of magnetic, 
electrical, and ponderable masses, 

ri2., /=/x — 0-, the older view — 

previous to Faraday's researches — 
considered m and m! the masses 
(ponderable or imponderable), and 
the distance r to be variable, fi a 
constant, corresponding to the gra- 
vitation constant. As stated above, 
the gravitation constant is, so far 
as we know, a real constant-— i.e., it 
is not affected by the nature of the 
medium which fills the space inter- 
vening between m and m', the at- 
tractive masses. Faraday doubted 
this ; but leaving gravitation — " as 
a relation by some higher quality " 
— aside, he directed his efforts to 
the testing of the validity of this 
view as regards electric and mag- 
netic action. He found that /x is 
not a real constant, but dependent 
on the nature of the medium and 
the objects which intervene be- 
tween the magnetic and electric 
masses. These researches, which 
are probably the first step in the 
direction of gaining by observation 
some notion of the mechanical 
manner in which action at a dis- 
tance is brought about, begin with 
the year 1837 (see 11th series of 
'Experimental Researches in Elec- 
tricity,' No. 1252). The result was 
that the "specific electric induction 
for different bodies" was estab- 
lished, contrary to the ideas of 

Poisson and others ('Exper. Res.,' 
No. 1167), and the word "dielec- 
tric" invented to denote the "action 
of the contiguous particles of the 
insulating medium" (No. 1168). 
From this point he was led a 
step farther, to ''expect that all 
polar forces act in the same general 
manner" — viz., by contiguous par- 
ticles. Faraday, however, is care- 
ful to remark that by contiguous 
particles he means those "which 
are next to each other, not that 
there is no space between them" 
(No. 1665). 

In 1838 Faraday was still doubt- 
ful whether magnetic action was 
similar in this respect to statical 
electric action ; but he thought it 
probable that it was "communi- 
cated by the action of the interven- 
ing particles" (No. 1729), and in 
pursuing this line of thought, in 
spite of many unsuccessful trials, 
he at last saw his ideas realised, 
discovered the magnetisation of 
light, and invented the term " dia- 
magnetic" to describe "a body 
through which lines of magnetic 
force are passing, and which does 
not by their action assume the 
usual magnetic state" (1845, 'Ex- 
per. Res.,' No. 2149). At the end 
of the 19 th series of researches he 
says: "In former papers (1838) I 
proposed a theory of electrical in- 
duction founded on the action of 
contiguous particles, . . . and I 
then ventured to suggest that prob- 
ably , . . magnetic action was also 
conveyed onward in a similar man- 
ner. At that time I could discover 






II! . 

Nevertheless, the fact that gravity, radiation, and 
electric and magnetic action appear as central emana- 
tions, decreasing with the square of the distance, — two 
properties which lend themselves to mathematical alid 
geometrical representation, — seemed to pave the way for 
further generalisations. All forces in nature were put 
down as central forces, either attractive or repulsive, and 
if not following the Newtonian formula, still dependent on 
the distance according to some mathematical expression. 
For nearly a century theoretical physics were occupied in 
working out the mathematical formulae expressive of these 
ideas, and Laplace himself promoted these attempts by the 
weight of his great authority. We do not possess the final 
views on this point with which the great mathematician 
intended to complete the last edition of his ' Exposition 
du Systeme du Monde ' ; but some of the later chapters of 
this work, treating of gravitation and molecular attraction, 
show us clearly in which direction he looked for progress 
in theoretical physics.^ 

no peculiar condition of the inter- 
vening or diamagnetic matter ; but 
now that we are able to distinguish 
such an action ; . . . now that 
diamagnetics are shown not to be 
indifferent bodies, I feel still more 
confidence in . . . asking whether 
it may not be by the action of the 
contiguous or next succeeding par- 
ticles that the magnetic force is 
carried onward," &c. (No. 2443). 
Faraday also made repeated experi- 
ments with the view of determin- 
ing how the force of gravitation 
is communicated, believing as little 
as Xewton did in an actio in distaiis, 
and he was wont to quote New- 
ton's words on this matter, refer- 
ring also to Euler's ether theory 
(No. 3305). 


^ In the fifth edition of the * Ex- 
position du Systeme du Monde ' La- 
place had suppressed these chapters, 
and had announced his intention 

to unite the principal results of 
the application of analysis to phe- 
nomena depending on a molecular 
action differing from universal at- 
traction " into a special treatise 
which should form a sequel to the 
'Exposition,' &c. This project was 
never carried out (see "avertisse- 
ment au sixieme edition de ' I'Ex- 
position ' "). The success which 
attended Laplace's attempts to ex- 
plain double refraction and aber- 
ration of light (following Newton's 
suggestions in the ' Principia ' and 
' Optics ' ) as well as capillary pheno- 
mena (following Haukesbee) left no 

The great prominence given by Laplace to the gravita- 
tional explanation of all natural phenomena, the fact that 
all the observable movements of the universe, the shape 
and size of the moving masses, and the orbits they de- 
scribe, as well as many phenomena observable on the 
surface of our globe, such as the aberration and refraction 
of light, the phenomena of the tides, of atmospheric pres- 
sure, and some of the more important molecular properties 
of matter, could be perfectly or approximately described, 
calculated, and predicted by gravitation or analogous at- 
tractions, gave to what we may call — following a hint 
of Clerk Maxwell's — the astronomical method^ of con- 

doubt in his mind that such pheno- 
mena "are owing to attractive and 
repulsive forces between molecule 
and molecule" ('Expos.,' 6"'« ed., 
p. 328). He saw in molecular at- 
traction the cause of the solidity of 
bodies, of chemical affinities, and of 
the properties of chemical satura- 
tion, which Berthollet had developed 
about that time ('Expos.,' p. 360) ; 
he thinks it likely that the law of 
molecular attraction is the same for 
all bodies, and he finally dwells on 
the question whether the attraction 
of gravity and molecular attraction 
could be united under one common 
law or expression (p. 363), and 
throws out the idea that thus the 
phenomena of physics and astro- 
nomy might be brought under one 
general law, adding, however, signi- 
ficantly, "Mais I'impossibilite de 
connaitre les figures des molecules 
et leurs distances mutuelles, rend 
ces explications vagues et inutiles h, 
I'avancement des sciences." 

^ "Cavendish, Coulomb, and 
Poisson, the founders of the exact 
sciences of electricity and magnet- 
ism, paid no regard to those old 
notions of 'magnetic effluvia' and 
' electric atmospheres ' which had 

been put forth in the previous 
century, but turned their undivided 
attention to the determination of 
the law of force, according to which 
electrified and magnetised bodies 
attract or repel each other. In this 
way the true laws of these actions 
were discovered, and this was done 
by men who never doubted that 
the action took place at a distance, 
without the intervention of any 
medium, and who would have re- 
garded the discovery of such a 
medium as complicating rather 
than as explaining the undoubted 
phenomena of attraction. . . . 
Ampere, by a combination of 
mathematical skill with experi- 
mental ingenuity, first proved that 
two electric currents act on one 
another, and then analysed this 
action into the resultant of a 
system of push - and - pull forces 
between the elementary parts of 
these currents. . . . "Whereas the 
general course of scientific method 
then consisted in the application 
of the ideas of mathematics and 
astronomy to each new investiga- 
tion in turn, Faraday seems to 
have had no opportunity of ac- 
quiring a technical knowledge of 







27. sidering nature a great impetus. As we have seien, it 

The astro- 
nomical was entirely an outcome of Newton's great discovery. 

view. '^ ^ -^ 

Soiar^tnd ^^ ^^ somctimcs uscf ul to distinguish between cosmical, 
phenomena. Dfiolar, and molccular phenomena ; it is, however, well to 
note that this distinction is a popular or practical, not a 
scientific one. The question, in how far pure magnitude 
affects the appearance and relations of the parts or ele- 
ments of which the universe is composed, is indeed of 
great scientific interest, but it has not yet received a 
definite answer. In the meantime we can use the term 
cosmical for such magnitudes of space, mass, or time as 
far transcend our own powers of direct measurement by 
the foot-rule, the balance, and the timepiece, and still 
more, our powers of direct action : those dimensions com- 
pared with which our own homes and actions absolutely 
disappear. We will call molar those masses which we 
can handle directly, those dimensions in which we build 
our own homes and pass our own lives. And we will 
call molecular those sizes and masses which on the other 
side are so small that the utmost powers of the micro- 
scope and the dividing machine fail to make them directly 
visible, still less tangible or manageable for our active 
powers. The lines which limit these three regions are 
indeed neither fixed nor fixable ; the middle region, which 

mathematics, and his knowledge of 
astronomy was mainly derived from 
books. . . . Thus Faraday was de- 
barred from following the course 
of thought which had led to the 
achievements of the French philos- 
ophers, and was obliged to explain 
the phenomena to himself by means 
of a symbolism which he could un- 
derstand, instead of adopting what 
■had hitherto been the only tongue 

of the learned" (Clerk Maxwell, 
"Action at a Distance," 'Proceed- 
ings of the Royal Institution,' vol. 
vii. Reprinted in 'Scientific Papers,' 
Cambridge, 1890, vol. ii. p. 317 sq. 
Cf. also vol. i. p. 156). Du Bois- 
Reymond uses the term "astro- 
nomical knowledge " in a somewhat 
wider sense in his discourse " Ueber 
die Grenzen des Naturerkennens " 
('Reden,' vol. i. p. 120). 

we may call our own home, seems to be extending through 
improved means of seeing and handling ; still every one 
has a vague notion, and science has supported this notion, 
that there are certain limits, marking the immeasurably 
large and the immeasurably small, which we cannot tran- 
scend. Now it is a question of great scientific interest 
to what extent mere enlargement, such as the microscope 
makes familiar to us, would essentially alter the behaviour 
and appearance of things natural. Would the planetary 
or stellar systems, reduced in size many million times, 
present an aspect similar to the view we here enjoy of the 
inanimate matter on the surface of our earth, and would 
the molecular structure of microscopic objects, many times 
enlarged, differ essentially from that aspect ? Our present 
knowledge would lead us to say they would essentially 
differ. Certain phenomena or modes of motion seem, so 
far as we know, essentially characteristic of the molecular, 
others of the molar, others again of the cosmical world.^ 

^ Laplace has made a significant 
remark on this point. See 'Ex- 
position du Systeme du Monde,' 
6 ed., p. 319 sq. : "La loi de la 
pesanteur reciproque au carrd des 
distances . . . est celle de toutes 
les emanations qui partent d'un 
centre, telle que la lumiere ; il pa- 
rait meme que toutes les forces dont 
Taction se fait apercevoir a des 
distances sensibles, suivent cette 
loi : on a reconnu depuis peu, que 
les attractions et les repulsions 
<51ectriques et magnetiques decrois- 
sent en raison du carre des dis- 
tances, en sorte que toutes ces 
forces ne s'affaiblissent en se pro- 
pageant,que parcequ'elles s'etendent 
comme la lumiere ; leurs quantites 
^tant les memes sur les diverses 
surfaces sphdriques que Ton pent 

imaginer autour de leurs foyers. 
Une propriete remarquable de cette 
loi de la nature est que si les 
dimensions de tons les corps de cet 
univers, leurs distances mutuelles 
et leurs vitesses, venaient h, aug- 
menter ou a diminuer proportion- 
ellement ; ils decriraient des courbes 
entierement semblables a eel les, 
qu'ils d^crivent, et leurs apparences 
seraient exactement les memes ; car 
les forces, qui les animent, ^tant le 
resultat d'attractions proportion- 
elles aux masses divisees par le carre 
des distances, elles augmenteraient 
ou diminueraient proportionelle- 
ment aux dimensions du nouvel 
univers. On voit en meme temps, 
que cette propriete ne peut apparte- 
nir qu'h la loi de la nature. Ainsi, 
les apparences des mouvements de 





to molar 


And we cannot but be struck by the fact that only those 
dimensions which we call molar appear to be the abode 
of living and conscious beings. The cosmical world has, 
so far as we know, no inhabitant which can behold it in 
the same way as man beholds this planet, and the same 
obtains so far as we are acquainted with the molecular 
world. So far as our knowledge goes and is likely ever 
to reach, a special importance or dignity will therefore 
always belong to molar dimensions and masses. The pro- 
cess by which we try to picture to ourselves in tracings and 
models, constructed in molar dimensions, the behaviour 
and appearance of cosmical as well as molecular masses will 
always recommend itself, not only as the most practical, but 
likewise as the most interesting and plausible, for only by 
this procedure do these unreachable worlds become amen- 
able to direct observation and to the processes of experi- 
ment in the physical laboratory. It seems 'prima facie 
that the wealth of phenomena and the variety of different 
kinds of motion decrease as we ascend into the cosmical, 
or as we descend into the molecular world, giving way 
in the former to essentially uniform, though to many 
times multiplied modes of motion, and disappearing in 

I'univers sont independantes de ses 

dimeDsions absolues, comme elle3 

le sont, du mouvement absolu, 

qu'il peut avoir dans I'espace ; et 

nous ne pouvons observer et con- 

naitre que des rapports." This is 

easily seen. For if in the formula 

- m.m IT., 
/= — —^ the dimensions be all 

multiplied by Ky we get the new 

formula F= K^-» x — - , and the 

acceleration of a body moving round 

a centre like the sun would be 
T?v-7 = ir^""x— , which is only 

K times the acceleration , if 

n = 2. In another passage Laplace 
repeats the above statement in 
slightly different words: "L'uni- 
vers veduit successivement jusqu'au 
plus petit espace imaginable, offrir- 
ait toujours les memes apparences 
a ses observateurs " (p. 440). That 
this would not apply to molecular 
attractions or repulsions is evident. 


the latter in stable and self-repeating averages. Pos- 
sessed therefore, as we seem to be, of the greatest wealth 
and variety of observations and notions, we may — perhaps 
erroneously — conclude that we can grasp the simpler 
cosmical and molecular movements and phenomena by 
starting from molar, physical, or mechanical models.^ 

^ English naturalists have always 
excelled in this line of investigation, 
whereas foreign scientific literature 
has been rich in purely mathemati- 
cal deductions from formulae which 
contained no construirhare Vorstel- 
lung. And it is interesting to note 
that both lines of thought go back 
to Newton. Whereas Newton him- 
self believed in the possibility of a 
mechanical explanation or represen- 
tation of the gravitation formula, 
the second edition of the *Prin- 
cipia ' by Cotes can be looked upon 
as sanctioning the view that gravi- 
tation is an ultimate quality which 
must be accepted as such ; and as 
it was the second edition through 
which Newton's ideas became large- 
ly known on the Continent, it is 
not surprising that he was there 
accused of reintroducing the quali- 
tales occidtcB of the older metaphys- 
ics, which Descartes and others had 
successfully banished. Clerk Max- 
well says ("Action at a Distance," 
*Scieut. Pap.,' vol. ii. p. 316): 
"The doctrine of direct action at 
a distance cannot claim for its 
author the discoverer of universal 
gravitation. It was first asserted 
by Roger Cotes in his preface to 
the 'Principia,' which he edited I 
during Newton's life. According | 
to Cotes it is by experience that i 
we learn that all bodies gravitate, i 
We do not learn in any other way 
that they are extended, movable, 
or solid. Gravitation, therefore, ; 
has as much right to be considered 
au essential property of matter as 
extension, mobility, or impenetra- 

bility. And when the Newtonian 
philosophy gained ground in Europe, 
it was the opinion of Cotes rather 
than that of Newton that became 
most prevalent." In fact, philoso- 
phers could be divided into two 
classes — those who took the fact 
of gravity or the wider idea of a 
universal attraction as a beginning, 
and drew from this beginning all 
the possible mathematical and ex- 
perimental consequences which they 
could think of ; and those who, 
whilst admitting this process as a 
legitimate one, thought it neces- 
sary to go behind the assumed 
beginning and find a still more 
hidden mechanical reason for this 
admitted property. To the latter 
class belonged Newton himself, 
Huygens, Euler, and in modern 
times notably Faraday and his fol- 
lowers ; to the former class be- 
longed Daniel Bernoulli, who wrote 
to Euler, 4th February 1744, refer- 
ring to the ether theory of the lat- 
ter : " Moreover, I believe both that 
the ether is gravis versus solem and 
the air versus terram, and I cannot 
conceal from you that on these 
points I am a perfect Newtonian, 
and I am surprised that you ad- 
here so long to the principiis Car- 
tesmnis ; there is possibly some feel- 
ing in the matter. If God has been 
able to create an aniniam whose na- 
ture is unknown to us, He has also 
been able to impress an attractioncra 
universalem matericv, though such is 
attractio supra captuni, whereas the 
principia Cartesiana involve always 
something contra captum" (see 





\ I may, in passing, mention here that in the course of 
our century certain views have been put forward in pure 
mathematics, or rather in geometry, which make it con- 
ceivable, if not probable, that our ideas of space might 
not apply to immeasurably small or to immeasurably 
large dimensions.^ )vShould the future progress of thought 

Miething, 'L. Euler's Lehre vom 
Aether,' p. 30). In quite recent 
times a similar position has again 
been taken up by Paul du Bois- 
Reymond in his essay "Ueber die 
Unbegreiflichkeit der Fernkraft," 
in the * Naturwissenschaftliche 
Rundschau' (vol. iii. No. 14), and 
in his posthumous work, 'Ueber 
die Grundlagen der Erkenntniss in 
den exacten Wissenschaften ' (Tii- 
bingen, 1890), in which he adds 
action at a distance as a third 
" ignorabimus " or unknowable pro- 
blem to the two given in his 
brother Emil's address, " Ueber die 
Grenzen des Naturerkennens " 
(1872, reprinted in 'Reden,' vol. 
i. p. 105). On the Continent, 
about thirty years ago, the fruit- 
lessness of pursuing this problem 
seemed generally admitted. Helm- 
holtz in 1847 speaks of the initial 
assumption " that all actions in na- 
ture are to be reduced to attracting 
and repelling forces, whose inten- 
sity depends merely on the distance 
of points mutually acting on each 
other" {actio in distans), and Du 
Bois-Reymond repeats this in 1871 
in his address. But it is significant 
that Helmholtz, who (through his 
memoir on vortex motion in 1858) 
gave such an impetus to the me- 
chanical explanations of molecular 
forces, modified his views on this 
point (see his address on Magnus, 
1871, 'Vortriige und Reden,' vol. 
ii.); accordingly in the reprint of 
his memoir of 1847 he has accom- 
panied it with some significant re- 
marks on the necessity of that 
initial assumption (1881, 'Wissen- 


schaftliche Abhandlungen,' vol. i. 
'. 68). 

^ Reimann was probably the first 
give expression to this line of 
thought. His memoir on this sub- 
ject, ** On the Hypotheses which lie 
at the Foundation of Geometry," 
bears the date 1854. It was read 
before the Philosophical Faculty of 
Gottingen in the presence and at the 
request of Gauss, on whom it made 
a profound impression (see the bio- 
graphical notice on Reimann by 
Dedekind, attached to Riemann's 
* Gesammelte Werke,' Leipzig, 1 876). 
The memoir was not published till 
after Riemann's death in 1867. In 
England the late Prof. Clifford in- 
troduced the subject to the Cam- 
bridge Philosophical Society in 1870 : 
" The axioms of plane geometry are 
true within the limits of experiment 
on the surface of a sheet of paper, 
and yet we know that the sheet is 
really covered with a number of 
small ridges and furrows, upon 
which these axioms are not true. 
Similarly although the axioms of 
solid geometry are true within the 
limits of experiment for finite por- 
tions of our space, yet we have no 
reason to conclude that they are 
true for very small portions ; and 
if any help can be got thereby for 
the explanation of physical pheno- 
mena, we may have reason to con- 
clude that they are not true for 
very small portions of space" (see 
Clifford's * Mathematical Papers,' 
p. 21. Compare also his lectures 
on "The Philosophy of the Pure 
Sciences " in ' Lectures and Essays,' ' 
vol. i. p. 295 sqg.) 


or observation bring forward any indications that the 
idea is not only a theoretical possibility, but an actual 
reality, then the mode of thought now so successfully 
used — viz., that of transferring phenomena belonging to 
molar dimensions, and exemplified in the physical lab- 
oratory, into cosmic or molecular space by a process of 
enlarging or of reducing — would become inapplicable. 
Mathematics indeed would not fail, but our ordinary 
geometry and the physical model and mechanism would 
fail: we should probably still be able to calculate, 
though not to represent, those phenomena of immeasur- 
able dimensions.^ 

As it is, the first great example of calculating and pre- 
dicting the phenomena of an unreachable world was 
Newton's successful attempt to explain the movements 
of the moon, and other cosmical bodies, by using the 
phenomena of falling bodies on the surface of the earth 
described by Galileo and Huygens ; and he was rewarded so. 
by the discovery of a universal law of attraction, which meaSg''^ 
would probably never have been discovered by experi- diS'eV'''' 
ments carried on within molar dimensions, the mass of 
the earth being so immeasurably greater than that of 
any molar masses under our control. It quite escapes 
our observation that in the action and reaction of the 
falling stone the immensity of the earth's mass is com- 
pensated by the vanishing distance through which the 
earth moves when attracted by the stone. Thus the 
astronomical view came to the rescue of physical or molar 
experiments, helped to explain them, and indicated the 
manner in which cosmical forces could be measured 
even on the surface of the earth. The pendulum experi- 
VOL. I. 2 






ments of Eicher, Halley, and many others, the measure- 
ments of the arc of the meridian, and Cavendish's and 
Maskelyne's experiments, were some of the direct results 
of the discovery. 

It was natural that, having explained the cosmical, and 
subsequently many terrestrial phenomena, successfully by 
the formula of attraction, Newton himself, and still more 
Laplace and his school, should have attempted the ex- 
planation of molecular phenomena by similar methods. 
31. The astronomical view spread into molar and molecular 


moiSf Physics. Newton himself made use of the notion of 
phenomena, molccular attraction ^—i.e„ of attraction existing only at 


^ In the fourteenth section of 
the first book of the 'Principia' 
Newton is, however, careful to speak 
always of "attractio vel impulsus," 
leaving it open to the reader to 
form his own opinion whether it is 
an action at a distance or a "vis a 
tergo," a push. He says also that 
the particles of light approaching 
solid bodies with a definite velo- 
city are bent, "quasi attracti in 
eadem (i.e.y corpora)." And in the 
twenty -third query to the first 
Latin edition of the 'Opticks' 
(1706) he says: "May not the 
small particles of bodies have cer- 
tain virtues, powers, or forces by 
which they act at some distance, 
not only on the rays of light, re- 
flecting, refracting, or inflecting 
them, but also on each other, pro- 
ducing various natural phenomena ? 
For it is sufficiently known that 
bodies mutually act on each other 
through the attraction of gravity 
and through magnetic and electric 
virtue. And these examples show 
what is the order and reason of 
nature, so that it becomes very 
probable that there may be other 
attractive forces. For nature is 
very similar and agreeing to her- 

self. Through what efficient cause 
these attractions are brought about 
I do not inquire here. What I 
here call attraction may well be 
produced by an impulse or in some 
other way unknown to us. I take 
this word attraction here in this 
way, that it be understood merely 
to mean some universal force with 
which bodies try to approach each 
other, whatever cause this force 
I may have to be attributed to. For 
from the phenomena of nature it 
behoves us first to be taught which 
bodies attract each other, and what 
are the laws and properties of this 
attraction, before we inquire by 
what efficient cause this attraction 
is brought about. The attraction 
of gravity and of the magnetic and 
electric virtue extend to sufficiently 
large distances, so that they fall 
under the notice of the vulgar 
senses ; but it may be that there 
are others which are contained in 
such narrow limits that they have 
so far escaped all observation." 
And he goes on to speak of the de- 
liquescence of some salts and of 
chemical combinations of finely 
powdered substances. And fur- 
ther on in the same query, after 


very small distances— to explain the refraction and in- 
flection of light passing from empty space, or from the 

referring to attractive forces acting 
only at small distances, he pro- 
ceeds : * * And as in algebra, when 
the positive quantities disappear 
and cease, negative quantities be- 
gin ; so in mechanics, where attrac- 
tion stops, there a repelling force 
must come in. But that such a 
force exists, seems to follow from 
the reflection and inflection of the 
rays of light. For the rays are 
repelled by bodies in both these 
cases, without the immediate con- 
tact of the reflecting or inflecting 
body. And if all this is so, then 
the whole of nature will be very 
simple and similar to herself ; per- 
forming all the great motions of 
the heavenly bodies by the attrac- 
tion of gravity, which exists be- 
tween all those bodies, and almost 
all the smaller motions of their 
particles through some other at- 
tracting and repelling force, which 
exists mutually between those 
particles" {' Optice,' mdccvi., p. 
341). The suggestions of Newton 
regarding forces of molecular di- 
mensions were taken up by other 
contemporary writers and experi- 
mentalists, and the 'Philosophical 
Transactions' during the early 
years of the last century contain 
several memoirs touching on this 
subject, notably by John Keill 
(1708), who refers to Newton's 
'Opticks,' and enlarges, as does 
also John Freind ( ' Prelectiones 
Chymicae'), on the usefulness of the 
idea of molecular attraction in ex- 
plaining chemical and physiological 
phenomena. In the later editions 
of the ' Opticks,' evidently in con- 
sequence of the elaborate experi- 
ments of Hauksbee, Newton enters 
more fully into the question of 
molecular, especially capillary, ac- 
tion ; and his last query, No. 31, is 
quoted by Laplace in his 'Theorie 

de I'Action capillaire,' which forms 
the supplement to the tenth book 
of the ' Mecanique celeste.' I may 
here mention that as some confu- 
sion exists in the different editions 
of the * Optics ' regarding the num- 
bering of the " Queries," it is best 
to refer to Horsley's Collected Edi- 
tion of the Works of Newton, 
where the latest English edition is 
reprinted, and all the variations 
and additions noted from the first 
(English) edition through the sub- 
sequent ones. The first edition 
breaks off with query 16 ; the first 
Latin one with query 23, and this 
was in later editions numbered 31, 
a number of new queries being in- 
serted, Nos. 18 to 24, referring to 
the " probability of a medium more 
subtle than air" and the *' me- 
chanical efficient of gravity." This 
was added "to show" (Newton's 
words in preface dated 16th July 
1717) "that I do not take gravity 
for an essential property of bodies, 
. . . choosing to propose it by way 
of a question, because I am not 
yet satisfied about it by way of 
experiments." We may note that 
this was written a few years after 
the second edition of the 'Principia ' 
was published by Cotes, whose 
preface did a good deal to occasion 
the misunderstanding regarding 
Newton's views on gravitation as a 
primary quality of matter. From 
his correspondence with Cotes, 
edited by Eddleston (1850), we 
know that Newton is composing 
the *' Scholium generale," which is 
added to the second and later edi- 
tions of the 'Principia,' had in- 
tended to say "much more about 
the attraction of the small par- 
ticles of bodies," but that on second 
thoughts he abandoned this inten- 
tion (p. 147). 





atmosphere, into or in the neighbourhood of solid bodies. 
He conceived light to be a material substance, consisting 
of minute particles, propelled in straight lines from the 
luminous centres. These small particles, when arriving 
at or near the surface of transparent bodies, came under 
the influence of an attraction from the substance of such 
bodies, and Newton succeeded in showing that for rays 
of light which fall on transparent surfaces at an angle, 
the path of the ray in the body would be deflected accord- 
ing to the rule experimentally determined by Snell, and 
published by Descartes. This application of the idea of 
attraction, or action at a distance, to very small or mole- 
cular dimensions, required a modification of the gravita- 
tion formula. The first who took an important step farther 
in this direction was Francis Hauksbee. Between the 
year 1709 and 1713 he made a series of experiments on 
what is called capillary action. His experiments were 
discussed by Newton in the later editions of the ' Opticks,*" 
and followed by thdse of Dr Jurin in 1718. Hauksbee,. 
Newton, Jurin, and subsequent writers, like Clairaut, all 
attributed these and similar phenomena to molecular 
attractions, and Laplace showed that for the mathematical 
treatment of the subject a knowledge of the exact law 
(corresponding to the Newtonian law of molar attraction) 
was unnecessary, but that it was necessary and sufficient to 
assume the existence of an attraction of the molecules of 
bodies, which decreases very rapidly as their distances in- 
crease, " so as to become insensible at the smallest distances 
perceptible by our senses." ^ The phenomena of atmos- 

^ See * M^canique celeste,' vol. temps, U determiner les lois d'at- 
iv. (1805), Supplement, p. 67. See traction qui representent ces ph^- 
also p. 2 : " J'ai cherche, il y a long- nomenes : de nouvelles recherches- 


pheric refraction as well as those of cohesion and adhesion 

of bodies — ^.e., the attraction of particles of the same or of 

different matter under what is commonly called contact or 

at distances which we call in science molecular — were thus 

submitted to calculation, and the results brought largely 

into harmony with experience.^ The problem presented 

itself and occupied natural philosophers all through the 

last century, whether a more general law of action at a 

distance could be found which comprised the phenomena 

of molecular as well as of molar attraction. 

The most celebrated attempt in this direction is that 33. 

of the Jesuit Eoger Boscovich, who in 1758 published an extension ot 

the Newton- 
elaborate treatise on this subject. lan formula. 

m'ont enfin conduit h faire voir 
qu'ils 8ont tons repr^sentes par les 
memes lois qui satisfont aux phe- 
nomenes de la refraction, c'est-Ji-dire 
par les lois dans lesquelles I'attrac- 
tion n'est sensible qu'a des distances 
inseusibles ; et il en resulte une the- 
orie complete de Taction capillaire." 
^ The terms insensible and im- 
perceptible, which are commonly 
used in these discussions, must be 
taken with caution. It is now 
known that, though not directly 
perceptible or sensible, the distance 
through which molecular action 
takes |)lace is measurable. Plateau 
in Belgium (1843 and following 
years) and Quincke in Germany 
(1868) made experiments on inde- 
pendent lines, and came to very 
similar results. The distance of 
molecular action appears to be about 
the twenty thousandth part of a 
millimetre. See Clerk Maxwell's 
article on Capillary Action in the 
9th edition of the 'Ency. Brit.,' 
reprinted in 'Scientific Papers,' 
vol. ii. ; also VioUe's ' Cours de 
Physique,' German edition, vol. i. p. 
591, &c., and p. 639. 

^ Roger Joseph Boscovich, of the 
Society of Jesus (1711-87), took up 
the ideas thrown out by Newton in 
the last query to the ' Opticks,' and 
published in 1758 at Vienna an 
elaborate treatise with the title 
* Theoria Philosophise Naturalis re- 
dacta ad.unicam legem virium in 
Natura existentium. ' A second 
edition was published at Venice in 
1763. His speculations begin with 
the year 1745, when he hit upon 
his general view that all forces in 
nature can be reduced to the action 
of indivisible and inextended atoms, 
endowed with inertia and with a 
mutual force which at vanishing 
distances is repulsive, which at in- 
sensible distances alternates accord- 
ing to some mathematical formula 
between repulsion and attraction, 
and, finally, at sensible distances 
becomes identical with Newton's 
force of gravitation. The general 
form of the curve which exhibits 
this action at a distance is given, 
and the algebraical formula dis- 
cussed, in the Supplement. But 
it was, of course, impossible to 
define the law any further. The 




Though many of the views contained in this treatise 
were really the same as those embraced by a large school 
of Continental mathematicians till far into this century, 


the book was almost completely forgotten on the Con- 
tinent.^ No real progress has indeed been made in the 
explanation of physical phenomena by the application of 

whole treatise is really more of a 
philosophical than a mathematical 
or experimental investigation. A 
large portion is taken up in de- 
fending his view against possible 
objections, and in showing how it 
agrees vnth or differs from the 
philosophies of Leibniz and New- 
ton. Whilst this treatise represents 
in general a view largely held by 
Continental philosophers of nature, 
it does not contain any new mathe- 
matical methods such as the ' Prin- 
cipia' contained before and La- 
place's 'Mecanique celeste' later, nor 
does it contribute any experiments 
such as those works likewise con- 
tained and suggested to others. 
In fact, it is more a metaphysical 
than an exact treatise, and as such 
has exerted no lasting beneficial 
influence on the progress of science. 
" The eighteenth century made a 
school of science for itself, in which 
for the not unnatural dogma of the 
earlier schoolmen, 'matter cannot 
act where it is not,' was substituted 
the most fantastic of paradoxes, 
contact does not exist. Boscovich's 
theory was the consummation of 
the eighteenth - century school of 
physical science. This strange idea 
took deep root, and from it grew 
up a barren tree, exhausting the 
soil and overshadowing the whole 
field of molecular investigation, 
on which so much unavailing 
labour was spent by the great 
mathematicians of the early part 
of our nineteenth century. If 
Boscovich's theory no longer cum- 
bers the ground, it is because one 
true philosopher required more light 
for trax;ing lines of electric force" 
(Sir William Thomson's Lecture 
before the Royal Institution, May 
1860. Reprinted in * Papers on 

Electrostatics and Magnetism,' 2nd 
ed., 1884, p. 224). Nevertheless it 
is extraordinary to note that Bos- 
covich's theory was more popular 
among British than among Con- 
tinental physicists. In France the 
book seems to have been little ap- 
preciated, although Boscovich was 
well known through his optical and 
astronomical researches (see Montu- 
cla's ' Histoire des Mathematiques,* 
vol. iii. p. 490, vol. iv. p. 188) ; and 
his differences with d'Alembert were 
notorious. But French science was 
then occupied less with metaphysi- 
cal theories than with mathematical 
analysis and experimental research. 
In Germany the book remained 
unknown, probably because Euler's 
authority favoured an opposite 
theory. In this country, however, 
the theory is often referred to from 
the time of Priestley ('History of 
Optics ') to Faraday (" On the Na- 
ture of Matter," ' Phil. Mag.,' 1844, 
vol. 24), and more recently Thom- 
son (Lord Kelvin). The last has 
probably more than any other living 
writer of similar eminence referred 
to Boscovich, whose theory he con- 
siders suggestive, and we are in- 
debted to him for the first serious 
attempt to establish by actual cal- 
culation the real capabilities of the 
Boscovich atoms in explaining the 
properties of chemical molecules, 
their stability and degree of satur- 
ation (see the Report of the 
British Association at Liverpool, 
1896). In Scotland Boscovich's 
theory was fully discussed in a 
posthumous article on "Corpuscular 
Forces " by John Robison, Professor 
of Natural Philosophy at Edinburgh, 
and published by Brewster in the 
1st volume of Robison's ' System of 
Mechanical Philosophy ' (Edinburgh, 

1822). His ' Elements of Mechani- 
cal Philosophy' (Edinb., 1804) be- 
tray, according to Dugald Stewart, 
"a strong and avowed leaning to 
the theory of Boscovich" (Works 
by Hamilton, vol. v. p. 107). The 
theory probably found favour, 
among other reasons, because it 
seemed to give support to the pre- 
valent corpuscular theory of light, 
which Euler opposed, as he did 
simple action at a distance. In 
the Scotch school of philosophy, 
of which Dugald Stewart was the 
most popular exponent, Boscovich 
was well known. Stewart refers to 
him frequently (Works by Hamilton, 
vol. ii. pp. 50, 107, 110, 343 ; vol. 
iii. p. 233 ; vol. v. p. 93 sqq. ; vol. 
vii. p. 173 sqq.) He quotes Priest- 
ley, Robison, and James Button as 
followers of Boscovich, whilst his 
own adherence is certainly very 
qualified, and he makes a very 
pertinent remark in his Introduc- 
tion to the ' Elements of the Philo- 
sophy of the Human Mind' (1792) : 
' ' I cannot help taking this oppor- 
tunity of remarking that if physical 
inquirers should think of again em- 
ploying themselves in speculations 
about the nature of matter, instead 
of attempting to ascertain its sen- 
sible properties and laws (and of 
late there seems to be such a ten- 
dency among some of the followers 
of Boscovich), they will soon involve 
themselves in an inextricable laby- 
rinth, and the first principles of 
physics will be rendered as mys- 
terious and chimerical as the pneu- 
matology of the schoolmen" (vol. 
ii. p. 50). Boscovich seems to have 
been fond of tracing mathematical 
curves to represent all kinds of pro- 
cesses, such as the intellectual ad- 
vancement of the age, and he shows 

graphically that this was declining 
(Dugald Stewart's quotation in his 
'Dissertation,' Works, vol. i. p. 499). 
^ When Fechner published the 
first edition of his * Atomenlehre ' 
( Isted., Leipzig, 1855 ; 2nded., 1 864), 
he does not seem to have known of 
Boscovich's treatise (see p. 229 of 
the 2nd edition), and it was simi- 
larly unknown to the Dutch meteor- 
ologist Buys Ballot, whose curves 
of the attracting and repelling 
forces of matter agree almost ex- 
actly with those of Boscovich (see 
' Fortschritte der Physik,' 1849. p. 
1 sqq. ; also Rosenberger's * Ge- 
schichte der Physik,' vol. iii. p. 536 
sqq. ) In French scientific literature 
the treatise of Boscovich is mostly ig- 
nored — the * Grande Encyclopedie ' 
does not even give its title. In 
fact, French science does not con- 
sider itself beholden to the cele- 
brated Jesuit for what I call the 
astronomical view of matter. See 
St Venant in ' Comptes Rendus, ' 
vol. 82, p. 1223: " Plusieurs auteurs, 
soit anglais, soit allemands, dans 
ses oeuvres qui sont du reste d'une 
haute portee, . . . se sont pris a 
condamner vivement, sous le nom de 
theoine de Boscovich, non pas son 
ideecapitale de reduction des atomes 
h, des centres d'action de forces, 
mais la loi m^me, la loi physique 
generale des actions fonctioiis des 
distances mutuelles des particules 
qui les exercent r^ciproquement les 
unes sur les autres. Et ils attri- 
buent ainsi au cdl^bre religieux 
Verreur grave oi sont tombes, sui- 
vant eux, Navier, Poisson et nos 
autres savants, createurs, il y a un 
demi-siecle, de la mecanique mole- 
culaire ou interne. Or cette loi 
bldmee, cette loi qui a et^, mise en 
(Buvre aussi par Laplace, &c., et 



Boscovich's or similar formulae, though the idea of action 
at a distance between the minute particles of matter un- 
derlies the theories by which Poisson, Navier, Cauchy, 
Lam^, and others calculated the effect of elastic forces in 
solid bodies, or the phenomena of light passing through 
transparent and crystalline substances. A different school 
of physicists, starting from ideas of a different kind, with 
which we shall become acquainted hereafter, have shown 
that specific notions as to the molecular structure of bodies 
are not required in order to deal with the phenomena 
referred to. Nevertheless, the idea of action at a distance 
governing the movements of immeasurably small, as it 
seemingly does those of immeasurably large masses in 
aature, received a great support by the development of 
two other branches of science, which belong essentially to 
the history of the present century. 

The sciences of electricity and magnetism can be said 
to have originated with Coulomb's accurate measure- 
ments with the torsion -balance. With this instrument 
he measured the attracting and repelling forces of 
bodies, electrified or magnetised, by comparing them 
with the mechanical forces required to twist a metallic 
wire. In this way he fixed what have ever since his 
time been termed the units of electricity or magnetism, 
reducing these quantities to the same system of measure- 
ment with which we measure the masses or inertia of 

Extended by moviug bodics. His methods were adopted and modi- 
Gauss and n J ^ 1 i> 

Weber. tied and greatly perfected by Gauss and Weber the 



prise par Coriolis et Poncelet pour 
base de la mecanique physique, 
n'est autre que celle de Newton lui- 
meme, comme on le voit dod seule- 

ment dans son grand et principal 
ouvrage, mais dans le scholie gen- 
eral de sa non moins immortelle 


former applying them to the measurement of the mag- 
netic forces of the earth, the latter to that of the forces 
exerted by currents of electricity — i.e., by electricity 
which is not at rest but in motion. As I have already 
stated, the measurements of Coulomb confirmed the 
prevalent notion that action at a distance, varying 
inversely as the square of the distance, and directly in 
the proportion of the quantities of the acting substance, 
was a universal formula or law of nature.^ The idea 

5 J> 

^ Coulomb's exact measurements 
of the attraction and repulsion at a 
distance of electrified bodies and of 
magnets were published during the 
years 1784 to 1789 in seven memoirs 
presented to the Paris Academy of 
Sciences. They are conveniently 
collected, together with some other 
memoirs of Coulomb, Poisson, and 
others on kindred subjects, in the 
. first volume of the 'Collection de 
Memoires relatifs a la Physique,' 
published in 1884 by the Soci^te 
fran9aise de Physique. Coulomb 
made use of the torsion-balance 
and the proof-plane, the actions of 
which he carefully examined. He 
confirmed the law, which had been 
vaguely or approximately expressed 
by various writers before him, that 
electrified bodies act on each other 
with a force which is proportional 
to the inverse square of their dis- 
tances. This he did by direct 
measurements of the repulsion of 
small electrified bodies in the tor- 
sion-balance (1785, 1st Memoire). 
He then extended his measure- 
ments by an indirect method to 
the action of electrified bodies of 
larger size and to magnets (2nd 
Memou-e). He also defined what 
is meant by quantity and density 
of electricity and magnetism, and 
showed how these could be meas- 
ured and how the action of elec- 
trified bodies and magnets depended 

on the more or less of these quan- 
tities. Coulomb's researches con- 
tain experiments of great delicacy. 
Although the laws which bear his 
name appear so simple when written 
down, the phenomena they repre- 
sent are most complicated, as in 
the case of electricity the effect of 
electrical influence, called by Fara- 
day induction, and in the case of 
magnetism the presence of the 
earth's magnetism, and the fact 
that we have never to do with one 
kind of magnetism but always with 
two states, destroys all chance of ex- 
hibiting experimentally the simple 
case represented by the mathemati- 
cal formula. It was therefore ne- 
cessary to consider this formula as 
being merely a convenient descrip- 
tion of the elementary action of 
supposed isolated quantities of 
electricity and magnetism, and by 
a process of summation to deduce 
mathematically the actual effects 
for such cases of interaction as 
are actually observable in the la- 
boratory. It was especially the 
phenomena of the distribution of 
electricity on the surface of elec- 
trified bodies of simple shape and 
the distribution of magnetic forces 
in the neighbourhood of magnets 
which had to be calculated and 
measured. In physical astronomy 
a similar course of reasoning and 
observation combined had verified 




of mass, which in the Newtonian formula' meant merely 
the quantity of matter, had indeed to be enlarged, and 
to the attracting forces had to be added those of re- 
pulsion; still, though physically the phenomena were 
entirely different, the mathematical expression which 
ruled the two electric and the two magnetic quantities, 
usually termed fluids, looked very much like the New- 
tonian gravitation formula : it betrayed philosophers into 
thinking they possessed an explanation where really they 
had only a measurement and a description.^ 

Newton's elementary law of gravita- 
tion, Laplace as it were summing 
up the evidence in his great work. 
What Laplace did for Newton was 
done by Poisson for Coulomb's ele- 
mentary law of electric and mag- 
netic action, and on a still larger 
scale by Gauss, who worked out 
the mathematical theory and ap- 
plied it to the case of the magnetic 
distribution on the earth's sur- 
face. In England, already before 
Coulomb's researches were pub- 
lished, Cavendish had, likewise by 
a combination of experiment and 
calculation, established the elemen- 
tary formulae and properties of 
electrical phenomena. See note to 
the following page. 

' The exact measurements of 
Coulomb and the mathematical 
analysis of Poisson and Gauss 
superseded the vaguer discussions 
on the nature of electricity and 
magnetism which were very fre- 
quent before that period, just as 
the mathematical principles of 
Newton and Laplace drove into 
the background the discussion on 
the nature and cause of gravity. 
Coulomb himself does not profess 
to settle the controversy caiTied on 
between the two schools of which 
Dufay and Franklin can be con- 
sidered as the principal representa- 

tives— W-., whether there existed 
two electric fluids or only one. 
Coulomb judged the rival views, 
simply as to their usefulness in 
describing and measuring phenom- 
ena : " Comme ces deux explications 
n'ont qu'un degr^ de probabilite 
plus ou moins grand je previens, 
pour mettre la the'orie ... a 
I'abri de toute dispute systdmatique, 
que dans la supposition des deux 
fluides ^lectriques je n'ai d'autre 
intention que de presenter avec le 
moins d 'elements possibles, les r^- 
sultats du calcul et de I'exp^rience, 
et non d'indiquer les veritable* 
causes de I'electricit^ " ('Collection 
de Me'moires,' vol. i. p. 252). He 
had previously, in 1777, rejected 
the theory of vortices to explain 
magnetic phenomena : " II semble 
qu'il resulte de I'experience que ce- 
ne sont point des tourbillons qui 
produiseut les diff^rents phdnom- 
enes aimantains, et que, pour les 
expliquer, il faut udcessairement 
recourir a des forces attractives et 
r^pulsives de la nature de celles, 
dont on est oblige de se servir pour 
expliquer la pesanteur des corps et 
la physique celeste" (vol. i. p. 8). 
And in 1789 he is still more 
cautious ; " Pour ^viter toute dis- 
cussion, j'avertis ... que toute 
hypothese d'attraction et de rdpul- 


The extension and confirmation which the Newtonian 
attraction formula had thus gained in the minds of 
many seemed to be entirely upset by a series of dis- 
coveries in which electrical, and subsequently magnetic, - 
phenomena played an important part. These were, the 
discovery of galvanic electricity by Galvani in 1791 and 
by Yolta in 1800; of the physiological and chemical 
effects of this form of electricity, especially by Davy 
(1806); of the magnetic effect of moving electricity by 
Oersted in 1820; of the connection of heat and elec- 
tricity by Seebeck in 1822; of induction by Faraday in 
1831 — i.e., of the action of electric currents and magnets 
in generating other electric currents or magnetic effects 
in bodies which are moving in their neighbourhood ; and, 
finally, of diamagnetism by Faraday in 1845. 

Many of the celebrated men with whose names the mod- se. 
ern discoveries in electricity are identified, and amongst Faraday, 
them notably Davy and Faraday, were not brought up 
in the mathematical school of the Continent,^ in which 

sion suivant une loi quelconque ne 
doit etre regardee que comme une 
formule qui exprime un resultat 
d'experience " (vol. i. p. 297). 

^ To these must be added the 
name of Cavendish (1731-1810), 
whose electrical researches, in 
which he anticipated many of Cou- 
lomb's results, proceeded on en- 
tirely different lines from those of 
the Continental school. He proved 
—in or before 1773— from the fact 
that a small globe situated in the 
hollow of a large electrified globe 
and communicating with it showed 
no signs of electricity, that electric 
attraction and repulsion must be 
inversely as the square of the dis- 
tance. In his published and post- 

humous papers (edited by Max- 
well in 1879 under the title of 
' The Electrical Researches of the 
Hon. Henry Cavendish') he anti- 
cipated, as Maxwell has shown, 
many later investigations of British 
and Continental writers. He had 
a clear notion of electrical capacity, 
of potential and of electrical resist- 
ance, he anticipated Ohm's law — 
i.e., the proportionality between 
the electro-motive force and the 
current in the same conductor. 
He studied the properties of diel- 
ectrics, and "not only anticipated 
Faraday's discovery of the specific 
inductive capacity of different sub- 
stances, but measured its numer- 
ical value in several substances " 




the astronomical view of phenomena had been established 
and strengthened mainly by a development of the New- 
tonian philosophy. They belonged to another school, 
which approached that great field of research from the 
purely experimental side, — mainly, so far as Davy was 
concerned, from the side of chemistry, which, dealing 
with the qualitative, not merely the quantitative, proper- 
ties of matter, was at that period almost entirely thrown 

upon experimental research.^ Chemistry had only just 
entered the list of the exact sciences, by the use of the 
balance, largely owing to Lavoisier and his followers. 

(Maxwell's Introduction to the 
'Researches,' p. xlix sqq.) Caven- 
dish's electrical work seems to have 
remained unnoticed abroad. Cu- 
vier, who fully appreciates him as 
a pioneer in modern chemistry, 
does not refer to his electrical 
researches, and in Continental 
works his name is hardly men- 
tioned in connection with elec- 
trical science. He, however, clearly 
belongs to the same lineage as 
Davy and Faraday, whose breadth 
of experimental observation some- 
what prevented them from fully 
assimilating the results of Coulomb 
and his school, which moved in 
narrower but more precise lines. 
If Cavendish was unknown abroad 
as an electrician, Coulomb was 
little known in England. Whewell, 
who did more than any other to 
make known the researches of the 
mathematical school (see his article 
in the * Encyclopaedia Metropoli- 
tana,' 1826, and his British Associ- 
ation Report, 1835), could state in 
the first edition of his * History of 
the Inductive Sciences' (1837) that 
" the reception of the Coulombian 
theory has hitherto not been so 
general as might have been reason- 
ably expected from its very beauti- 
ful accordance with the facts which 
it contemplates" (3rd ed., vol. iii. 
p. 28). He then refers to the ex- 
periments of Snow Harris. These 
experiments, as well as those of 

Faraday, carried on about the same 
time, dealt largely with the proper- 
ties of dielectrics and of what we 
now call the electric field, a subject 
almost entirely neglected by the 
mathematical school of that period. 
It was not till 1845 that William 
Thomson (Lord Kelvin) cleared up 
the whole subject in a memoir, 
** On the Mathematical theory of 
Electricity in Equilibrium " (see 
'Reprint of Papers.' &c., p. i5). 
He there refers to the fact that 
"many have believed Coulomb's 
theory to be overturned by the in- 
vestigations " of Snow Harris and 
Faraday, and he therefore pro- 
poses to show that "all the experi- 
ments which they have made hav- 
ing direct reference to the distri- 
bution of electricity in equilibrium 
are in full accordance with the 
laws of Coulomb, and must there- 
fore be considered as confirming 
the theory" (p. 18). He thus 
brought together the two inde- 
pendent lines of research and 
thought, the mathematical and the 
experimental, represented by the 
school of Gauss and Weber abroad, 
and by Faraday in England, and 
suggested those further researches 
of which Maxwell's 'Treatise on 
Electricity and Magnetism' is the 
great exponent. See the preface 
to this work, p. xi, &c., 1873 ; also 
Maxwell's ' Scientific Papers,' vol. 
ii. pp. 258, 302, 304. 

^ Although Faraday's ' Experi- 
mental Researches in Electricity' 
(1831-52) contain mostly what 
chemists would call ''qualitative" 
investigations and only few exact 
"quantitative" measurements — 
forming in this respect a very 
remarkable contrast to Weber's 
* Electrodynamische Maasbestim- 
mungen ' (1846-78) — it is important 
to remark that one of the methods 
for exact measurement of the 
electric current — viz., by the chem- 
ical decomposition of compounds 
— was established by Faraday in 
1833 and 1834. He showed that 
whenever decomposition took place 
the quantities decomposed were in 
proportion to the amount of elec- 
tricity flowing through the circuit 
and in proportion to the chemical 
equivalents. Owing to the want of 
a clear definition of quantity and 
intensity of current, Berzelius op- 
posed this view of Faraday's as 
illogical, confounding the quan- 
tity of substance decomposed with 
the force required to set it free. 
Clearer definitions and accumu- 
lated experience have confirmed 
Faraday's law, which is now 
looked upon as one of the best es- 
tablished general facts of chemical 
and electrical science. Somewhat 
earlier than Faradav, Georg Simon 
Ohm established (l'827, 'Die gal- 
vanische Kette, mathematisch 
bearbeitet') the proportionality of 
the quantity of electricity passing 
through a circuit with the electro- 
motive force in the same conductor, 
introduced the notion of electrical 
resistance, and showed how this 
varies as the length and inversely as 
the thickness of the same conductor, 
and is different in different con- 
ductors. The accuracy of Ohm's 

law, though elaborately tested by 
Fechner and confirmed by Pouillet, 
was frequently doubted ; in France 
it met with tardy recognition, and 
in England some of the most im- 
portant researches — such as those of 
Faraday — were carried on without 
reference to it. In the first edition 
of Whe well's History it is not men- 
tioned. When the second edition 
was published (1847), Ohm had 
received the Copley Medal of 
the Royal Society (1841), and 
Wheatstone had besides in the year 
1843 drawn attention to the clear 
definitions which Ohm had intro- 
duced. The opinion has been ex- 
pressed that Ohm found his law by 
theoretical considerations based on 
analogy with the flow of heat in 
conductors, and that he subse- 
quently proved it experimentally. 
The pubhcation of Ohm's collected 
papers by Lommel ('Gesammelte 
Abhandlungen,' Leipzig, 1892), how- 
ever, disproves this opinion ; as his 
experimental measurements had 
during 1825 and 1826 — not without 
some initial mistakes — led him to 
the well-known expression of the 
relations of the different quantities 
(see Lommel's Introduction, p. vii). 
Whereas in Germany it was a pure- 
ly scientific interest — that, namely, 
of subjecting physical phenomena 
to mathematical calculation — which 
induced Ohm, Gauss, and Weber 
to devise instruments and methods 
for exact measurement, it was in 
England mainly the practical re- 
quirements of telegraphy which 
created the desire for clear defini- 
tions and exact methods. With 
these requirements in view Wheat- 
stone invented his instruments and 
drew attention to the definitions of 
Ohm. See his Bakerian Lecture for 





Yet the great variety, more than the exact measurement 
of phenomena, attracted the attention of natural philoso- 
phers in this new field. And when through Davy,Berzelius, 
and Faraday in different ways the importance of electric 
action in chemical processes became established, it was 
natural that from this school an entirely different view of 
electrical and magnetic phenomena should emanate : we 
may term it — in opposition to the astronomical — the phys- 
ical view of phenomena. This view, which, as the astron- 
omical view had done, found later on its expression in a 
mathematical formula, will occupy our attention in a sub- 
sequent chapter. It has in the course of the second half 
of the century very largely expelled the other and rival 
view from the domain of molar and molecular physics. 
But the astronomical view, with its largely developed 
mathematical apparatus, was not easily defeated : it was 
AmplJ; and ^^^^^ ^^^^ ^^ grapple with even such complicated processes 
7^^\it ^^ ^^® discoveries of Oersted and Faraday had revealed, 
astronomi. [ j^ ^hc opiuiou of many Continental thinkers it won its 
greatest laurels when, under the treatment of Ampere in 
France and of Neumann and Weber in Germany, the 
perplexing interactions of magnets, diamagnets, and 

1843 ('Philos. Transactions,' 1843, 
p. 303, &c.) : "An energetic source 
of light, of heat, of chemical action, 
and of mechanical power, we only 
require to know the conditions un- 
der which its various effects may- 
be most economically and ener- 
getically manifested to enable us 
to determine whether the high ex- 
pectations formed in many quarters 
of some of these applications are 
founded on reasonable hope or on 
fallacious conjecture. " Forty years 
later Lord Kelvin, in his address 

"On the Electrical Units of Meas- 
urement" (1883; see 'Popular 
Lectures and Addresses,' vol. i. p. 
76), could still speak of the com- 
paratively recent date at which 
"anything that could be called 
electric measurement had come to 
be regularly practised in most of the 
scientific laboratories of the world," 
whereas such measurements had 
then been for many years "familiar 
to the electricians of the submarine 
cable factories and testing sta- 

electric circuits — the phenomena of electro-magnetism, 
diamagnetism, and induction — were all resolved into 
elementary processes of attraction and repulsion, and 
summed up in a formula which looked like an extension 
of the Kewtonian gravitation formula, revealing the 
mysterious influence of molecular forces.) 

" Oersted had found that an electric current acts on a 
magnetic pole, but that it neither attracts it nor repels it, 
but causes it to move round the current. He expressed 
this by saying that the electric conflict acts in a revolving 
manner. The most obvious deduction from this new fact 
was, that the action of the current on the magnet is not 
a push-and-pull force, but a rotary force, and accordingly 
many minds began to speculate on vortices and streams 
of ether, whirling round the current. But Ampere, by a 
combination of mathematical skill and experimental in- 
genuity, first proved that two electric currents act on one 
another, and then analysed this action into the resultant 
of a system of push-and-pull forces between the elemen- 
tary parts of these currents." ^ 

Weber in Germany took up the work where Ampere 
had left it.^ One of his objects was to combine the 

^ Clerk Maxwell "On Action at 
a Distance" ('Scientific Papers,' 
vol. ii. p. 317). 

^ Weber's interest was twofold. 
The primary object was to put 
accurate quantitative data in the 
place of merely qualitative descrip- 
tions or mere estimates of pheno- 
inena. He had then already pub- 
lished, together with his brothers 
(see supra, p. 196, note 3), two 
works in which in a similar way 
exact research has taken the place 
of inexact description. The first 

was his experimental investigation 
of wave-motion ('Die Wellenlehre 
auf Experimente gegriindet,' 1825), 
the other the still more delicate at- 
tempt to treat a physiological pheno- 
menon, the mechanism of the organs 
of locomotion, on exact mechanical 
principles (1836). This rare gift of 
exactness, invaluable at all times, 
but almost unique at that time in 
Germany, where philosophical vague- 
ness was only too common, attract- 
ed the notice of Gauss, who brought 
Weber to Gottingen in 1830 after 




Weber's fun 

different electric phenomena— those of electricity in the 
state of rest, called statical effects; those of electric 
currents on each other, the dynamical results ; and those 
of electric conductors in a state of motion, the pheno- 
mena of induction— in one general and fundamental 
formula or law. He had before him Coulomb's electro- 
static formula, Ampere's electro-dynamic formula, and a 
more general one established by Franz Neumann, which 
described and embraced not only the phenomena dis- 
covered by Oersted, but also those of moving conductors 
discovered by Faraday. It is not necessary here to enter 
into the details of the investigations, experimental and 
mathematical, by the aid of which Weber succeeded in 
establishing his very remarkable and seemingly all- 
embracing formula. Two remarks, however, present 
themselves, bearing upon the history of thought and the 
value of precise mathematical expressions. The first is, 
that as the gravitation formula necessitated a series of 
the most careful definitions and measurements of physical 
quantities, and the invention of accurate instruments and 
methods of measurement, so the first and probably the 
most valuable performances of Weber were his ingenious 
apparatus, and the careful measurements by which he 

the death of Tobias Mayer. Gauss 
introduced Weber to his own exact 
measurements of terrestrial magnet- 
ism, and from hence Weber's own 
line of thought led through the 
phenomena of magneto - induction 
(discovered by Faraday in 1831) 
and terrestrial magneto - induction 
(1832) to electro - dynamics, the 
science which Ampere had created 
in the years 1820 to 1823. In 1846 
Weber speaks in the introduction 
to the * Electro-dynamische Maas- 

bestimmungen ' of the endeavour to 
determine natural phenomena ac- 
cording to number and measure, 
expressing surprise that this has 
not yet been done in electro- 
dynamics, and then proceeds to de- 
scribe his "electro-dynamometer," 
an instrument used by him for 
many years. With this instrument 
he then, further, proceeds to con- 
firm Ampere's formula for the action 
at a distance of the elements of 
electric currents. 


fixed the elementary conceptions and quantities with 
which he operated. All his researches were comprised 
under the very significant title " electro-dynamical mea- 
surements." As such they remain a great monument 
of ingenuity and unparalleled accuracy.^ The second 

^ Gauss had, some years before 
Weber commenced his electrical re- 
searches, introduced the idea of an 
absolute measure of other than 
mechanical forces — i.e., following 
up the definition of force in the 
Newtonian laws of motion, that it 
is the cause which brings about a 
change of motion, he suggested that 
every physical force can be measured 
by the velocity it imparts to a mov- 
able body of measurable mass, the 
quantity of mass being in the same 
locality measured by its weight ; 
and he applied this to the measure- 
ment of magnetic forces. In ap- 
plying the same idea to the measure- 
ment of electric currents, Weber 
came at once upon the circumstance 
that the forces exerted by an elec- 
tric current can be measured in 
two ways— viz., by the action they 
have upon magnets or by that 
which they have on other electric 
currents. Now by a familiar con- 
ception, electricians look upon a 
current of electricity as measur- 
able by the quantity of electric- 
ity which flows through a section 
of the circuit in a given unit of 
time, this quantity of electricity 
being measurable in the same way 
as Coulomb measured the action 
at a distance of charged bodies. 
Should it then be possible to 
carry out this latter measurement 
of an electric current, a comparison 
between the electro- magnetic and 
the known electro-static units of 
electricity would become possible. 
Faraday had already, in 1833 and 
1834, made estimates of the numer- 
ical relation of the quantity of 
electricity in a current, measured 

VOL. I. 

by its chemical or electro-magnetic 
efiects, and of the same quantity if 
produced by an electrical machine. 
These estimates were more than 
twenty years later, in 1856, reduced 
to accurate measurements by Weber 
and Kohlrausch. Through these 
measurements, which confirmed the 
enormous numbers which are re- 
vealed when we compare electricity 
at rest and electricity in motion, 
Weber finished the series of ac- 
curate measurements, reduced to 
an absolute or mechanical standard, 
which had been begun by Gauss in 
1833. It was soon recognised of 
what practical importance these 
data must be to electricians. Ac- 
cordingly the British Association at 
their meeting at Manchester in 1861 
appointed a committee, on the sug- 
gestion and under the presidency 
of Sir William Thomson, called the 
"British Association Committee of 
Electrical Standards." " This com- 
mittee worked for nearly ten years 
through the whole field of electro- 
magnetic and electro-static measure- 
ment, until in its final report, pre- 
sented to the Exeter meeting in 
August 1869, it fairly launched the 
absolute system for general use" 
(Thomson, * Popular Lectures and 
Addresses,' vol. i. p. 84). In recog- 
nition of Weber's great merit in 
first introducing this system into 
electrical science and practice, the 
name "Weber" had been selected 
by Latimer Clark for the unit of 
current. In the final fixing of the 
units in Paris in 1881 other units 
than those previously in use were 
adopted, and to avoid confusion the 
names were somewhat differently 





point I wish to urge is, how in those days the Newtonian 
formula was taken as the great model of a law of nature, 
and how the researches of Coulomb, Poisson, Ampere, and 
Weber stand in logical connection with the theory of 
gravitation. Let us see what Weber himself says on this 
subject:^ "After the general laws of motion had fur- 

nished a foundation, there remained in physics mainly the 
investigation of the laws of interaction of bodies; for 
without interaction bodies would for ever remain in that 
state of rest or motion in which they happened to be. 

chosen. This explains the fact, 
deplored by Weber's friends and 
admirers, that his name has dropt 
out of the list of terms now adopted 
throughoutthe civilised world. (See 
Wiedemann, 'Die Electricitat,' 
Braunschweig, 1885, vol. iv. p.* 
906, &c.) Recently 'Proi. Lodge 
has suggested the introduction of 
the names of Weber and Gauss to 
denote some of the derived units in 
the electrical measurements. See 
Brit. Assoc. Report, 1895, p. 197 n. 
1 Weber's theoretical conception 
of the nature of electric action at a 
distance is mixed up with his exact 
measurements of electrical quanti- 
ties, though these can be stated 
without making use of his theoreti- 
cal conceptions. It is the nature 
of the absolute system of measure- 
ment that it establishes numeri- 
cal relations based upon a small 
number of original units (space, 
time, and mass, or space and time 
alone, see note to p. 323 above) 
which are universally intelligible. 
Whatever, therefore, the theoretical 
views may be which led the investi- 
gation, in the end these are elim- 
inated in the system of original 
(primary) and derived (secondary) 
units. But Weber's theory com- 
mands attention for its own sake 
as the furthest stage to which 
the gravitational view of phenom- 
ena, provisionally introduced by 
Newton, has been pushed. It has 
been extolled and condemned, ac- 
cording to the favour with which 
the purely mathematical treatment 
of phenomena has been received. 

In the school of Laplace this purely 
mathematical treatment quite ob- 
scured all other views which did 
not minister to it. Thus Laplace 
remained to the end an adherent of 
the emission or corpuscular theory 
of light, and opposed the ideas of 
Young and Fresnel, who developed 
the dynamical view. In order to 
make the cosmical view of nature 
useful for the explanation of mole- 
cular phenomena, two distinct and 
definite conceptions, contained in 
the gravitation formula, had to be 
modified and enlarged. The con- 
ception of matter, which in physical 
astronomy is limited to gravitational 
matter, had to be extended so as to 
bring into calculation what was then 
called imponderable matter, such as 
light, heat, and electricity. And | 
the law of gravitation, which defines 
the purely attractive property of 
ponderable matter, had to be modi- 
fied so as to embrace also the repul- 
sive action observable in a certain 
class of phenomena. Coulomb had 
shown that ponderable matter 
charged with electricity followed 
the same formula for attraction 
and repulsion as gravitating bodies 
did : he simply adopted the two- 
fluid theory of electric matter. 
Poisson developed the mathematics 
of fluids, actuated by repelling forces 
depending on the inverse square of 
the distance. Oersted showed the 
action of electric currents on mag- 
nets ; and Ampere showed that 
magnets can in their action be sup- 
planted by electric currents. La- 
place very early satisfied himself that 

these actions of ponderable matter, 
in which electricity was flowing, 
could be reduced to an action at a 
distance proportional to the inverse 
square of the elements of the electric 
circuits. When Faraday showed 
that a current of electricity under 
certain conditions induced in con- 
ductors in its neighbourhood other 
currents, this was explained by 
saying that the electric fluid exerted 
not only pondero- motoric but also 
electro- motoric action at a distance. 
Not only did electrified matter act 
on other electrified matter, but 
electricity as a fluid acted on elec- 
tricity itself. Weber adopted, for 
the purpose of putting these ap- 
parent actions into mathematical 
language, and for finding an ele- 
mentary law of the ultimate par- 
ticles of electric matter out of 
which by summation the observ- 
able data might be calculated, the 
hypothesis of Fechner, according to 
which in an electric current the 
two electric fluids were moving 
with equal velocity in opposite 
directions. It then became evident 
— looking at the phenomena dis- 
covered by Oersted, Ampere, and 
Faraday — that the electro - static 
formula of Coulomb required to 
be supplemented by an additional 
term, if the mutual action was to 
be determined not only for the case 
of equilibrium and rest, but also for 
that of relative motion. The ad- 
ditional term, depending on this 
relative motion, had to be found. 
(See ' Electrodynamische Maasbes- 
timmungen,' vol. i. p. 102). From 
this starting-point, and with this 
definite problem in view, Weber un- 
dertook a series of most valuable 
measurements. No doubt can exist 

as to the lasting importance of these 
measuremen ts. Any theoretical con - 
ception which produces in its appli- 
cation such results must hold a 
prominent place in the history of 
scientific thought. And the very 
fact that, unlike Boscovich and 
other purely metaphysical theorists, 
Weber undertook to fix by experi- 
ment the actual constants or nu- 
merical quantities which his ab- 
stract formula contained, led to 
much enlargement of actual know- 
ledge. I will mention only one 
of the most interesting points in 
his elaborate researches. I stated 
above that it took a whole century 
after the discovery of the law of 
gravitation before the gravitation 
constant was approximately fixed, 
but that for the progress of phy- 
sical astronomy this was of little 
importance, gravity being a uni- 
versal property of matter. Still 
such a constant exists, because we 
possess another definition of matter 
— viz., inertia or mass. The con- 
stant in Coulomb's law cannot be 
determined in a similar manner, as 
the property of attraction or repul- 
sion defines for us ultimately the 
numerical quantity of electricity. 
We have — so far — no other ultimate 
absolute measure of electricity. But 
in Weber's law it was the quantities 
of electrical matter which acted on 
each other not only according to 
their distances, but also according 
to their relative motion or their 
velocities. A second constant thus 
entered into his formula, and this 
constant established a relation be- 
tween electricity at rest and elec- 
tricity in motion. This constant 
was a velocity, and, if determinable, 
it revealed a constant of nature in 




All changes of these states, and all phenomena depen- 
dent thereon, are therefore consequences of these inter- 
actions. But bodies exert such mutual actions when in 
contact as well as from a distance, and it was evident 
that a beginning had to be made with the latter in 
order to gain a clue for the investigation of the former ; 
this being especially needful whenever the spatial rela- 
tions of bodies escape observation, as is the case with 
bodies which are in contact. And so it has really 
happened, inasmuch as a beginning was made by ex- 
amining the mutual action of cosmic bodies — i.e., with 
the phenomena of gravitation. To this first field of 
research — viz., the phenomena of gravitation — there was 
then added the investigation of electric and magnetic 
interactions, as next to gravitation these are the only 
actions which take place from one body to another at 
measurable distances, — these actions being themselves 
measurable. Now for a long time Newton's doctrine 
of gravitation furnished the leading idea for nearly all 
theories of electricity and magnetism, till a new clue 
was gained through Oersted's and Ampere's discoveries 

the form of a velocity. It had 
for Weber a theoretical as well 
as a practical meaning, for it en- 
abled him to effect a connection 
between the electro-magnetic and 
the electro-static or absolute system 
of measurements. When he suc- 
ceeded in measuring this quantity, 
it was found that the figure for the 
constant, which meant a velocity, 
was practically the same as that for 
the velocity of the propagation of 
light. Weber himself does not seem 
to have attached any physical mean- 
ing to this coincidence : later he and 
Kirchhoff remarked that under cer- 

tain conditions an electrical wave- 
motion might take place in an 
electrical conductor, and that the 
velocity of the propagation of this 
would coincide with that of light 
(see Kirchhoff in ' Annaleu der Phy- 
sik uud Chemie,' 1857; and Weber, 
'Electrodyn. Maasbest.,' 1864). It 
was reserved for Clerk Maxwell to 
point to the real physical interpre- 
tation of Weber's constant. Of 
this I shall speak in a later chapter 
(see Maxwell's memoir ' On Physical 
Lines of Force,' 1862, reprinted in 
* Scientific Papers,* vol. i. ) 

regarding the equivalence of closed electrical currents 
with magnets. This led, first, to the reduction of all 
magnetic effects to the action of electrical currents ; and, 
secondly, to the enunciation of a fundamental law of the 
interaction of two elements of electricity in motion. A 
third leading idea was that of reducing the interaction 
of all bodies to that of the mutual action of pairs of 
bodies. This idea could in general be considered as 
well established and confirmed by experience on a large 
scale." ^ 

This leads me to another and a final remark on the 
view of natural phenomena, first introduced by New- 
ton's gravitation formula, which has been so success- 
ful in the calculation of all the movements of cosmic 
bodies, and which in the eyes of such a great authority 
as Laplace contained the clue to an explanation also of 
molar and molecular phenomena.^ This view calculates 

Necessity of 
the infini- 

^ * Electrodynamische Maasbes- 
timmungen,' 1878, p. 645. 

2 Although Weber followed the 
lines so deeply impressed upon the 
whole of Continental thought by 
the labours of Laplace and his 
school, it does not seem that he 
held the same exalted opinion of 
the value of any mathematical for- 
mula as ^ did Laplace. Though he 
looked upon his electro - dynamic 
law as well established by experi- 
ment and valuable in guiding 
further research, he was fully im- 
pressed with the fact that all such 
formulae are merely provisional. 
Thus he says in the first part of 
his researches, written in the year 
1846: "It seems to follow that 
the immediate interaction of two 
electrical particles does not depend 
upon these alone, but also upon the 
presence of third bodies. ... It is 

conceivable that the forces com- 
prised in the discovered funda- 
mental law may be partly the 
forces which two electrical particles 
exert indirectly on each other, and 
which therefore depend on the in- 
tervening medium. . . . The general 
law for the determination of the 
acting forces might perhaps be yet 
more simply expressed by taking 
the intervening medium into ac- 
count, than has been possible 
without it in the fundamental 
law now established. The explora- 
tion of the intervening medium, 
which might afford an insight into 
many other matters, can alone give 
an answer to this question. ... A 
hope now exists that it will be 
possible, in several new ways, to 
gain some information as to the 
neutral electric fluid which per- 
vades everything. Perhaps in 





the actions of large masses and complicated systems of 
bodies by a process of summation from the interaction of 
units placed in the simplest relation — that of two and 
two, pushing or pulling each other in a straight line. 
Now, in consequence of the great distances at which we 
are placed from the heavenly bodies, these appear to us 
as mere points, and the observation of their movements, 
their orbits, and their periods enabled astronomers like 
Kepler, and mathematicians like Xewton, to gain by mere 
observation and subsequent calculation an idea of the 
elementary rule which masses, considered to be concen- 
trated in points, follow in their motion in a connected 
system. The next step was to see how these elementary 
actions would add up in cases where the dimensions of 
the moving bodies were not vanishingly small in com- 
parison with their distances. The infinitesimal methods, 
invented in the age of Newton, and developed by him 
and others into a special calculus, came to the aid of 
mathematicians, and enabled them to calculate from 
elementary data the motions and phenomena of extended 
bodies and systems of bodies. These could afterwards 
be actually measured, thereby confirming the elementary 
formulae and assumptions which had formed the basis of 
those calculations. As already remarked, this process 

other bodies, which are not con- 
ductors, there exist, not currents, 
but only vibrations, which may in 
future be observed by the methods 
indicated above. Further, I need 
only point to Faraday's recent dis- 
covery of the influence of electric 
currents on the vibrations of light, 
which makes it probable that the 
all-prevadiug neutral electric medi- 
um itself constitutes the all-prevad- 

ing ether which contains and pro- 
pagates luminous vibrations, or at 
least that the two are so intimately 
connected that the observation of 
luminous vibrations may aflford some 
information regarding the proper- 
ties of the neutral electric medium." 
He then refers to Ampere's own 
suggestion in this direction. ('Elec- 
Parti., p. 169.) 



of confiriliation occupied a long period, during which it 
became more and more satisfactory and complete. In 
fact, so great has the coincidence of calculation with 
observation turned out to be, in all problems of physical 
astronomy, that no astronomer at the end of this century 
doubts that the gravitation formula alone will suffice to ian formula 

o the basis of 

explain all anomalies which still exist in great number ^^tronomy. 
in the movements of cosmic bodies — such, for instance, 
as the moon./ 

Moreover, in the whole wide range of physical and 
chemical, not to speak of other natural phenomena, there 
is probably no instance of a simple mathematical rela- 
tion having been applied to so large a field of facts, 
found so trustworthy a guide, and been so unfailingly 

And yet the very extent of this field must not blind 
us to the fact that for the explanation of molecular^ 

^ This is indeed not to be won- 
dered at when we consider that in 
all molecular and molar phenomena 
such a variety of elements and forces 
come into play that it is impossible 
to isolate any special quantities as 
we do when from the cosmic point 
of view we lose sight of everything 
except mass, time, and distance — 
i.e., the elementary factors of our 
system of measurement. In the 
phenomena of electricity, for in- 
stance, it is merely bj' a process of 
mental abstraction, which has no 
counterpart in the observable phe- 
nomena, that we speak of electrical 
masses, be they one or two ; of 
fluids ; of elements of currents, 
which in nature cannot exist alone ; 
of velocities of a something which 
as yet cannot be clearly defined. 
Any mathematical formula can 
under such conditions be merely 

tentative, and the preciseness of it 
must not hide from us the fact that 
it is based upon hypothetical rela- 
tions and artificial definitions. This 
was, for the gain of scientific 
thought, very clearly brought out 
in the theoretical discussions which 
followed upon Helmholtz's critical 
examination of Weber's and kindred 
formulae, and is well expressed by 
Carl Neumann: "Electrical mat- 
ters" — if such there be — "never 
exists alone, but only in combina- 
tion with ponderable matter." Any 
law like that of Weber can there- 
fore be merely a " particular," not 
a "fundamental" or "universal" 
law, for it refers merely to a small 
portion of the properties, forces, 
and relations of electric and pon- 
derable matter, leaving others — as,, 
for instance, those between electric- 
ity and heat, electricity and light. 




phenomena, or even for such processes as happen con- 
tinually under our eyes and our hands, this universal 
law of gravitation has practically done nothing. The 
action of gravitation alone between masses which we 
can manipulate directly is so weak that it takes the very 
finest instruments to detect it at all, and ac molecular 
distances it is so immeasurably small that it is hardly 
conceivable how it can explain the existence of those 
enormous forces with which we here have to deal.^ If 

&c. — more or less in the dark (see 
• Mathematische Annalen,' vol. xi. 
p. 323). From a philosophical point 
of view these discussions, in which 
many other eminent leaders of 
scientific thought took part, are 
of great interest and importance, 
as they bear upon the value of 
mathematical formulae in physical 
research, upon the definition of 
laws of nature, the extent of their 
applicability, the correct lines of fut- 
ure research, the use of analogies in 
the formation of physical theories, 
&c. I therefore refer here to the 
literature of the subject: Tait, 
' Sketch of Thermodynamics ' (1868, 
pp. 57, 76); Thomson and Tait, 
'Natural Philosophy' (1st ed., p. 
311); Carl Neumann, 'Die Prin- 
cipien der Electrodynamik ' (Tiib- 
ingen, 1868) ; Helmholtz in various 
memoirs from 1872 onwards, all 
collected in * Wissenschaftliche Ab- 
handlungen' (vol. i. pp. 545, 636, 
774, &c.) and in * Vortriige und 
Reden ' (vol. ii. Faraday Lecture) ; 
Carl Neumann, ' Mathematische 
Annalen' (vol. xi. p. 318). See 
also Riecke on * Wilhelm Weber' 
(Gcittingen, 1892), and Clerk Max- 
well, 'Electricity and Magnetism,' 
(vol. ii. last chapter) ; ♦ Elementary 
Treatise on Electricity ' (p. 51). 

^ An interesting speculation as to 
whether the Newtonian formula of 
gravitation is capable of explaining 

cohesion and capillary attraction 
will be found in Thomson's (Lord 
Kelvin's) paper to the Royal Society 
of Edinburgh (1862), and in his lec- 
ture before the Royal Institution 
(1866), on Capillary Attraction, both 
reprinted in the first volume of 
' Popular Lectures and Addresses.' 
He there shows that if we combine 
Newton's law with the assumption 
of an ultimate heterogeneousness of 
matter, — as is demanded in the so- 
called atomic theory used in chem- 
istry,— the mass of ultimate por- 
tions of matter at vanishing dis- 
tances, or what is called in contact, 
may give rise to molecular forces of 
attraction of any magnitude ; since 
the Newtonian attraction depends 
on two data — the distance and the 
density (or mass) of attracting par- 
ticles. He concludes by saying that 
"it is satisfactory to find that, so 
far as cohesion is concerned, no 
other force than that of gravitation 
need be assumed" (p. 63). It does 
not seem that this view, which was 
also held by Sir John Herschel, is 
generally adopted by physicists (see 
Todhunter and Pearson, 'History 
of the Theory of Elasticity,' vol. i. 
p. 418, &c. ; vol. ii. art. 1650). An- 
other interesting speculation arose 
out of the discussion over Weber's 
law. One of the objections started 
by Helmholtz against Weber's law 
was that, under certain conditions, 


for the purpose of discovering the forces which exist in 
the universe between cosmic bodies we had been con- 
fined to experiments in the laboratory, as we are in all 
other departments of physics and chemistry, it is very 4i. 
doubtful whether this universal law of gravitation would Jan formuiJ* 

, . ^ unique as to 

ever have been discovered. And yet it stands there as universality 

•z ana accur- 

almost the only formula universally applicable to all ^''^* 
matter throughout the visible and tangible imiverse. 

In the foregoing pages I have sometimes spoken of this 
great discovery of Newton, on which is based the astron- 
omical view of nature, as a formula, sometimes as a law. 
A formula is merely the expression in definite terms of 
certain relations of measurable quantities. By a law 
we are apt to understand something more — viz., the 
statement of some fundamental, all-pervading property 
of the things of nature, which, so far as we are con- 
cerned, is final.^ Whether the human mind is at all 

this expression would give an in- 
finite value for the force between 
electrical particles in motion. 
Weber replied that the same argu- 
ment could be used against the 
gravitation formula, and hinted at 
the possibility that a correction 
might have to be added to the New- 
tonian formula to make it appli- 
cable to molecular distances ( ' Elec- 
trodyn. Maasb.,' 1871, p. 60). This 
idea was taken up by several Con- 
tinental mathematicians (see Isen- 
krahe, ' Das Riithsel von der Schwer- 
kraft,' p. 33, &c. ; Paul du Bois- 
Reymond, 'Ueber die Grundlagen 
der Erkenntniss,' p. 50 ; Tisserand, 
'Comptes Rendus,' September 1872). 
^ Helmholtz says, referring to 
Weber's so-called law: "If we 
are to consider Weber's law as an 
elementary law, as an expression 
of the ultimate cause of the phe- 

nomena to which it refers, and not 
merely as an approximately correct 
expression of facts within narrow 
limits, then we must demand that, 
if applied to objects of the largest 
imaginable dimensions, it should 
give results which are physically 
possible" (1873, 'Wissenschaftliche 
Abhandlungen,' vol. i. p. 658). This 
sentence raises a philosophical ques- 
tion as to the demands which we 
can legitimately expect to be satis- 
fied by any so-called law of nature 
expressible in the symbols of hu- 
man thought, be these words or 
algebraic signs. I venture to think 
that nowadays, and largely in con- 
sequence of discussions similar to 
those carried on over Weber's law, 
physicists do not any longer expect 
to find laws of that general and 
fundamental character which the 
words given above describe. 






Is the New- 
tonian for- 
mula an 


capable of finding out the ultimate properties of things, 
is a question which has been answered in opposite 
ways. But whatever the answer may be to this philo- 
sophical question, the further and more modest ques- 
tion can be raised, Does the gravitation formula express 
one of those universal facts which we have to accept 
as final, beyond or behind which we cannot penetrate ? 
Opposite answers have been given to this question. But 
it stands very much in the same position in which 
Laplace left it when he said : ^ " The extreme difficulty 
of the problem referring to the system of the universe 
obliges us to have recourse to approximations, which 
leave room for the fear that the neglected quantities 
may have a sensible influence on the results. As soon 
as mathematicians by observation became aware of this 
influence they returned to their analysis : by rectifying 
the same they have always found the cause of the ob- 
served anomalies ; they have determined the laws of 
these, and frequently they have outrun observation by 
discovering irregularities which had not yet been ob- 
served. The lunar theory, the theory of Saturn, of 
Jupiter and his satellites, offer many examples of this 
kind.^ Thus we may say that nature herself has helped 
in perfecting the astronomical theories founded upon the 

^ Exposition du Systeme du 
Monde,' 6th ed., p. 318. 

'^ Tisserand, in discussing the diffi- 
culties which still beset the lunar 
theory, and after referring to the 
"prix Damoiseau " offered by the 
Academy of Sciences for an essay 
on this subject, says ( ' Bulletin 
astronomique,' 1891, vol. viii. p. 
501): "La th^orie de la lune se 

trouve arret^e par la difficult^ que 
nous venons de d^velopper ; dejh, 
k r^poque de Clairaut la gravita- 
tion universelle paraissait impuis- 
saute a expliquer le mouvement 
du perigee; elle triomphera encore 
du nouvel obstacle qui se presente 
aujourd'hui, mais il reste k faire una 
belle d^couverte." 

principle of universal gravitation. This is, in my opinion, 
one of the greatest proofs of the truth of this admirable 
principle. As to this principle, is it a primordial law 
of nature ? Is it only a general effect of an unknown 
cause ? Here the ignorance in which we are as to the 
ultimate properties of matter stops us, and removes all 
hope that we shall ever be able to answer these questions 
in a satisfactory manner." 

In the meantime, as I have tried to show, the clue 
afforded by this principle has led physicists by strict 
analysis, by observation, by cleverly arranged experi- 
ments as well as by guesses drawn from analogy, to the 
discovery of many unknown phenomena, to the fixing in 
mathematical language of interesting relations, and in 
general to a large extension of the field of natural know- 
ledge. No wonder that a principle which has done, and 
is still doing, such valuable service in physical astronomy 
should have done much to establish the astronomical 
view of nature.^ As one of the latest representatives of 
physical science abroad has said, " The present generation 

^ This view was concisely put by 
J Poisson at a time when the corpus- 
,^ cular theory of the imponderables 
( —light, heat, and electricity — still 
reigned supreme in the Continental 
school: "Toutes les parties de la 
matiere sont soumises a deux sortes 
d'actions mutuelles. L'une est at- 
tractive, independante de la nature 
des corps, proportionnelledu produit 
des masses, et en raison inverse du 
carre des distances: elle s'etend 
indefiniment dans I'espace, et pro- 
duit la pesauteur universelle et 
tous les phenomenes d'equilibre et 
du mouvement qui sont du ressort 
de la m^anique cdleste. L'autre 

est attractive et repulsive ; elle 
depend de la nature des particules 
et de leur quantite de chaleur ; 
son intensite decroit tres rapide- 
ment quand la distance augmente, 
et devient insensible, dds que la 
distance a acquis une, grandeur 
sensible " (' Journal de I'Ecole poly- 
technique,' cahier xx, p. 4, 1831). 
See also Clerk Maxwell, ' On the 
Equilibrium of Elastic Solids ' (1850, 
reprinted in * Scientific Papers,' vol. 
i. p. 30), where a similar assumption 
is stated as the basis of the mathe- 
matical theories of Navier, Poisson, 
Lame, and Clapeyron. 







is still more or less accustomed to think in the manner of 
Newton's view of nature, in which the supposition of 
forces acting at a distance appears as the most simple 
view: we feel it difficult to step out of this circle of 
ideas." ^ Nevertheless, the country itself which produced 

1 Kundt, * Die neuere Entwick- 
lung der Electric! tiitslehre ' (Berlin, 
1891, p. 35). This habit is prob- 
ably more marked on the Continent 
than in England. In this country 
the later developments of Laplace's 
astronomical view of nature have 
remained unknown except to a few 
scientific specialists. Through Fara- 
day's influence, and in consequence 
of the backwardness which the 
English school of science exhibited 
early in the century in a.ssimilating 
Continental ideas (see p. 232, note), 
theoretical views on electricity as 
well as on other forms of energy 
were formed and taught more in 
conformity with experimental ob- 
servation. I am not aware that 
Weber's theory was expounded in 
any English text-book or handbook 
before Maxwell referred to it as the 
view to which Faraday and he him- 
self were opposed. In fact, the 
astronomical view of molecular 
physics is almost entirely of foreign 
growth. In England " action at a 
distance" is now stigmatised as a 
pernicious heresy (Tait, * Properties 
of Matter,' 2nd ed., 1890, Introduc- 
tion) or as unthinkable (0. Lodge, 
'Modem Views of Electricity,' 
1892, p. 386, &c.) Abroad weighty 
authoiities have pronounced against 
the astronomical view of nature as 
final or even helpful in the present 
stage of physical and chemical 
science. Helmholtz, who was 
trained in it, gradually emanci- 
pated himself, probably under the 
influence of physiological studies ; 
so did Kirchhoff, who in his lectures 
on Electricity (edited by Planck, 
1891) hardly mentions Weber's law. 

though he had previously, in 1857, 
based an elaborate and valuable 
investigation upon it (* Ueber die 
Bewegung der Electricitat in Drah- 
ten,' ' Gesammelte Abhandlungen,' 
p. 131, &c.) Still more marked is 
the aversion to the attitude or 
habit of thought which belongs to 
the astronomical view of nature on 
the part oi those who approached 
physical problems from the side of 
chemistry. Hittorf (quoted by 
Lehmann, ' Molecularphysik,' vol. ii. 
p. 456) explains the opposition of 
Berzelius to Faraday's electrolytic 
law and to his other results from 
the fact that they stood in direct 
opposition to that view " which at 
the end of the last century had 
been introduced into chemistry 
through the success of Newton's 
law in astronomy, and under the 
influence of Laplace on I^avoisier 
and Berthollet," and sees the im- 
portance of his own laborious 
researches in the demonstration 
"that the mysterious potential 
energy cannot in the case of un- 
combined chemical substances be 
explained by the work of attractive 
forces," and "that a confession of 
ignorance in such matters is more 
conducive to progress than the as- 
sertion that every process in nature 
is essentially a phenomenon of at- 
traction in the Newtonian sense." 
Of Ostwald's endeavours to liberate 
theoretical views in chemistry from 
the tyranny of the older hypotheses 
I shall have frequent occasion to 
speak. His discourse ' Die Energie 
und ihre Wandlungen ' (Leipzig, 
1888) contains an expression of 
opinion similar to those quoted here. 


the author of this the astronomical view of nature has a. 


also been the birthplace of a different manner of regard- to the astro- 


ing physical phenomena. It will be the object of a future J^atur? 
chapter to trace the origin and growth of what I propose 
to call the physical view of nature. We shall then learn 
how the germs of this different view can be traced even 
in the writings of Newton. But before I take up this 
subject I must deal with another and independent way 
of regarding nature which very largely supplemented the 
astronomical view. If the Newtonian gravitation formula 
is the basis and principle of physical astronomy — of our 
knowledge of cosmic phenomena — the view I am now 
going to explain has been equally useful in building up 
another most important science of modem times — the 
science of chemistry. 





1. / 




In the last chapter I have shown how, under the influence 
of the Newtonian philosophy, the ancient but indefinite 
ideas of Attraction and Eepulsion acquired a definite 
meaning, and how— at least so far as cosmical phenom- 
ena are concerned— the Newtonian Gravitation formula 
was made the foundation of very successful explanations ^ 

I use the word explanation in 
conformity with the popularly ac- 
cepted meaning of the term. It is, 
however, well to remark here that, in 
the course of our century and greatly 
owing to the influence of the exact 
scientific spirit, a change is being 
gradually introduced into language, 
which will assist in conveying more 
correct views as to the objects of 
science. In England the meta- 
physical interest has been so long 
banished from scientific literature, 
the part also which experiment and 
observation have played has been 
80 great, that misunderstandings as 
to the real objects of science have 
been less frequent than abroad, 
especially in Germany, where the 
metaphysical or philosophical in- 
terest still largely pervades scien- 
tific literature, though metaphysics 
themselves may be on the decline. 
There the definition of the science 

of mechanics (now more usually 
termed dynamics in this country), 
given by KirchhoflFin his ' Vorlesun-"7 
gen uber mathematische Physik ' i 
(vol. i. p. 1), has marked quite an h 
epoch in the philosophy of the ex- 
act sciences. This definition is as 
follows : ' ♦ Mechanics is the science 
of motion ; we can assign as its 
object : to describe completely and 
in the simplest manner the motions 
which occur in nature." Inas- 
much as a large school of natural 
philosophers consider that it is the 
object of all exact sciences to give 
a mechanical explanation of natural 
phenomena, it would follow that 
the object of all science is to re- 
duce the phenomena of nature to 
forms of motion, and to describe 
these completely and in the simplest 
manner. We may feel some re- 
luctance in assenting at once to 
this definition. Still an analysis of 

of nature. Towards the end of the last century, and all 
through the present one, this view of things natural, which 
I have called the Astronomical view, has exerted a great 
fascination over scientific minds : especially in the mathe- 
matical schools of France and the Continent it has been 
a leading idea in scientific thought. It has been ex- 
tended into molar and molecular physics, and has in 
these led to some very extraordinary and ingenious 
theories. In England, this astronomical view of Nature 
has, in the course of the present century, been received 

what has been done since Newton 
in real science will probably con- 
vince us that the definition is safe 
and sufficient. It means the an- 
alysis of phenomena as to their 
appearance in space and their se- 
quence in time. Both can, in con- 
sequence of the small number of 
elementary relations on which 
arithmetic, geometry, and dynam- 
ics are built up, be reduced to 
— or described in — a small num- 
ber of elementary terms or concep- 
tions, the alphabet of all science. 
To show how in every instance the 
terms of this alphabet are to be put 
together, in order to correspond to 
any phenomenon, is all the explana- 
tion we can give. Objections have 
been raised to Kirchhoff's definition 
by Du Bois-Reymond (" Gothe und 
kein Ende," in 'Reden,' vol. i. 
p. 434), inasmuch as it does not 
define the difference between the 
descriptive (historical) and the ex- 
act (mathematical) sciences of na- 
ture ; but the difference is really 
maintained if we demand a com- 
plete description. Natural history 
only affords an incomplete descrip- 
tion. The only complete descrip- 
tion is that afforded by a mathe- 
matical formula in which the con- 
stants are supplied by observation. 
This permits us to calculate those 

features or phases of phenomena 
which are hidden from our obser- 
vation in space or in time. An 
objection to the view which identi- 
fies physics with mechanics, seems 
implied in Mach's remarks con- 
tained in the last chapter of his 
very thoughtful book 'Die Me- 
chanik in ihrer Entwickelung ' 
(Leipzig, 1889). According to his 
view, the aim of exact science is 
not necessarily to give mechanical 
explanations or descriptions of phe- 
nomena, inasmuch as temperature, 
electric potential, &c., are just as 
simple elements of natural phenom- 
ena as mass and motion. It seems, 
nevertheless, that exact measure- 
ments are only possible in the 
data of time and space. Assum- 
ing that a complete and simple 
description — admitting of calcula- 
tion — is the aim of all exact science, 
it is evident how much and how 
little we may expect from science. 
We shall not expect to find the 
ultimate and final causes, and 
science will not teach us to under- 
stand nature and life. The search 
after ultimate causes may perhaps 
be given up as hopeless ; that 
after the meaning and significance 
of the things of life will never be 
abandoned : it is the philosophical 
or religious problem. 




with less favour, although it was entirely owing to 
Newton's gravitation formula that it ever obtained its 
gi^eat influence, the labour of Continental men of science 
being very largely spent in two directions : first, in draw- 
mg the purely mathematical consequences of Newton's 
formula— in this they have met with increasing success, 
unparalleled by that in any other domain of science;' 
and secondly, in extending the principle of Newton, by 
experiment and analogy, into other departments. In some 
of these, very remarkable results have been achieved ; but 
nevertheless at the end of the century no extension or 
analogue of the Newtonian gravitation formula has been 
generally accepted, and it still stands there as almost 
the only firmly established mathematical relation, ex- 
pressive of a property of all matter, to which the' pro- 
gress of more than two centuries has added nothing, 
from which it has taken nothing away. The value,' 
however, of all those partial attempts in another direc- 
tion has been enormous ; for with the aim of applying, 
extending, or modifying a rigorous mathematical for-' 
mula, those philosophers have carried out a series of 
the most exact observations and measurements of physi- 
cal quantities, very greatly extended our knowledge of 
natural phenomena and their mutual relations, and 
founded that general system of physical measurement 
which IS now universally adopted. The names of Gauss 
and Weber stand out prominently as leaders in this 
work. I shaU have to come back to this point later 
on, after I have shown that other views of nature 
besides the astronomical have also led up to it, and 
placed it in similar prominence. 






About a century after the publication of the ' Principia/ 
which, by propounding the gravitation formula, raised the 
ancient and indefinite notion of Attraction to the rank of 
a useful and rigorously defined expression, another favour- 
ite theory of the ancient philosophers ^ was similarly ele- 
vated to the rank of a leading and useful scientific idea. 

Although no mathematical relation equal in value and 
definiteness to the gravitation formula marks the intro- tS^! 
duction of the Atomic theory in Chemistry, it never- 
theless owes its success to similar qualities — m., to the 
fact that it led natural philosophers to make definite 
measurements, and put exact research in the place of 
vague reasoning. 

The atomic theory, usually associated with the name 
of Dalton, is, however, not nearly as much the historic 
property of that great man as gravitation is that of 
Newton, for whereas the latter gave the fullest gen- 
eralisation that can so far be safely made, the atomic 

^ Ancient philosophers have fur- 
nished us with three distinct ab- 
stractions which have survived, and 
which, put into definite mathemati- 
cal language, have led exact research 
in physics and chemistry in modern 
times — the theory of Attraction 
and Repulsion, the Atomic Theory, 
and the Kinetic Theory, or the 
notion that everything is motion. 
Of these three theories the second 
was most developed in antiquity ; 
Lucretius's great poem on the na- 
ture of things being really a treatise 
on the subject, in which the atomic 
view is placed in the centre, the two 
other ideas being likewise largely 
utilised. The historians of ancient 
philosophy trace these abstract or 
leading ideas back to the earlier 
Oreek thinkers. Thus Heraclitus 

VOL. I. 

of Ephesus is credited with having 
first taught that everything is in 
motion. Empedoclesof Agrigentum 
made use of the notions of Attrac- 
tion and Repulsion, poetically re- 
presented as Love and Hatred, to 
explain the action of his elements ; 
and Democritus of Abdera is uni- 
versally considered to be the true 
founder of the atomistic theory, 
which was adopted and developed 
in the School of Epicurus, and very 
fully explained by the Roman poet. 
A very good analysis will be found 
in Lange's ' History of Materialism ' 
(English translation by Thomas, 3 
vols.), in which also the historical 
connection with modem thought, 
especially through Bacon, Gassendi, 
and Hobbes, is clearly brought 












theory has been gradually defined and variously modi- 
fied in the course of this century, and is still in a sonie- 
what unstable condition. We are also bound to attach 
the greatest importance to the preliminary step taken 
by Lavoisier, who is even more justly called the father 
of modern chemistry than Kepler is called the father 
of modern astronomy. 

The exact claims of Lavoisier to this important place in 
the history of chemistry have been variously stated:^ 

^ Continental writers are pretty 
unanimous in dating modern chem- 
istry from the time of Lavoisier 
(1743-1794). In this country there 
has been less unanimity, the names 
of Black, of Cavendish, of Priestley, 
even of Robert Boyle, having occa- 
sionally been put* forward. The 
fact that Lavoisier did not suffi- 
ciently acknowledge ^ his indebted- 
ness to some of his English con- 
temporaries has given occasion in 
some quarters to depreciation of his 
merits. It cannot be upheld that 
he was the first formally to express 
the doctrine of the indestructibility 
or conservation of matter, as this 
idea underlay many experimental 
researches before his time ; nor 
that he was the first to refer to 
the balance as the ultimate test 
of chemical facts. The assertion 
that he first introduced the idea 
of two difierent kinds of matter, 
ponderable and imponderable, is 
also questionable, and still more 
so his claim to having discovered 
oxygen, the composition of water 
and of atmospheric air, the combus- 
tibility of the diamond, and other 
special facts. His fame rests upon 
a much broader basis, and has 
been most clearly investigated and 
settled by Hermann Kopp in his 
' Entwickelung der Chemie in der 
neueren Zeit' (Miinchen, 1873). 

In this excellent work the author 
somewhat modifies the view he 
took in his earlier * Geschichte der 
Chemie ' (Braunschweig, 1843, espe- 
cially vol. i. p. 274, &c.), and sums 
up Lavoisier's merit in the follow- 
ing words (p. 145): "His contem- 
poraries could dispose of the same 
inherited and much new material, 
but not one of them understood 
how to build up out of this material 
and his own independent researches 
a chemical system, the reception of 
which should form the starting- 
point for all future improvement 
of this science. Lavoisier has the- 
whole merit of having achieved 
this. He added to his own recog- 
nition of the correct views the work 
of procuring recognition for them 
from others. He imparted his own 
matured views to those who repre- 
sented chemistry at the end of the 
last century. . . . We must measure 
his greatness not merely by his 
own insight but also by the re- 
sistance which he had to overcome 
in other chemists who clung to- 
the older theory. These achieve- 
ments are great enough not to re- 
quire the exaggeration with which 
they have occasionally been an- 
nounced, and not to be touched by 
attempts on the other side to mini- 
mise them." 

there is however no difference of opinion on this point, 
that since his time, and greatly through his labours, the' 
quantitative method has been established as the ultimate 
test of chemical facts ; the principle of this method being 
the rule that in all changes of combination and reaction, 
the total weight of the various ingredients— be they ele-' 
mentary bodies or compounds— remains unchanged.) The 
science of chemistry was thus established upon an exact, 
a mathematical basis. By means of this method Lavoisier,' 
utilising and analysing the results gained by himself and 
others before him, notably those of Priestley, Cavendish, 
and Black, succeeded in destroying the older theory of 
combustion, the so-called phlogistic theory.i From a 

J_ This result was announced in 
1777 to the Paris Academy, and 
the demonstration completed in a 
memoir of 1783. "He closes this 
latter memoir with the expression, 
that his object had been to bring 
forward new proofs of his theory 
of combustion of 1777, and to 
prove that Stahl's phlogiston was 
something purely imaginary,— that 
without it facts could be more 
easily and more simply explained 
than with it; he did not expect 
that his views would be at once 
accepted, . . , time would have 
to confirm or to reject the opinions 
he had developed, but already he 
recognised with satisfaction that un- 
prejudiced students of the science, 
unbiassed mathematicians and phy- 
sicists, believed no longer in phlo- 
giston as Stahl viewed it, and that 
they considered the whole doctrine 
more as a hindrance than as a help- 
ful scaffolding in erecting the edifice 
of science" (Kopp, 'Entwickelung,' 
p. 202). This and the further re- 
mark of Kopp that it was the 
mathematicians who took up La- 
voisier's views (see supra, p. 115, 

note 2) are significant signs of the 
mtroduction of the mathematical, 
the measuring, spirit into chemistry! 
Few ideas which once exerted so 
great and lasting an influence on 
science as that of phlogiston, have 
so entirely disappeared from our 
text-books, and it is interesting to 
note that those whose researches 
were guided by it were not so far 
from grasping a valuable truth 
as has been supposed. This theory, 
elaborated by Stahl, a contem- 
porary of Newton and Leibniz 
(1660-1734), was the first attempt 
to co-ordinate a great mass of ob- 
servations, to bring the phenomena 
of chemical change under one com- 
mon principle. Phlogiston was 
the thing the migration of which 
gave rise to chemical change, and 
as the most obvious changes were 
exhibited in the processes of com- 
bustion, " Phlogiston " or " Brenn- 
stoff"" was the name which sug- 
gested itself as most suitable for 
this principle. Chemical changes 
were not to be measured so much 
by the resulting change of weight 
as by the readiness with which 









scientific point of view, the principal defect in this theory 
was, that its explanations could not be subjected to any 
strict and exact numerical verification. Whenever an 
element enters into our operations which has either no 
weight or a negative weight, and thus evades exact de- 
termination and control, explanations and observations 
become vague and uncertain. 

In the time of Lavoisier, and pre-eminently through his 

exertions, this vague and unmeasurable principle phlo- 

criston was eliminated from the laboratory and the text- 

books : quantities took the place of indefinable qualities, 

and numerical determinations increased in frequency and 

accuracy. The vague phlogistic theory, which contained 

a germ of truth, but one which at that time could not be 

put into definite terms, had helped to gather up many 

valuable facts and observations : these were collected and 

restated in a new and precise language. It has been said 

that every science must pass through three periods of 

development. The first is that of presentiment, or of 

faith ; the second is that of sophistry ; and the third is 

that of sober research. Liebig states the case somewhat 

substances enter into chemical re- 
action ; and the mobility or inert- 
ness of chemical substances was to 
be measured by the presence or ab- 
sence of a definite something. A 
hundred and fifty years after Stahl, 
science had so far advanced, that 
besides the change of weight or 
mass, the change of the power 
of entering into chemical com- 
bination could also be measured, 
and the term " potential energy " 
was introduced to describe many of 
those properties and processes which 
Stahl had fastened upon, when he, 
as the pioneer, undertook to co- 

ordinate chemical phenomena. If 
Stahl considered phlogiston to be 
a substance, though he did not in- 
quire into its mass or ponderable 
property, the question might be 
put again, whether " energy " is not 
to be considered after all as a sub- 
stance. Cf. Tait, 'Properties of 
Matter' (2ud ed., introduction, es- 
pecially p. 5 sqq.); 'Recent Ad- 
vances of Science,' introduction; 
also Clerk Maxwell, ' Electricity and 
Magnetism ' (last chapter) ; Ost- 
wald, 'Chemische Energie' (Leip- 
zig, 1893, p. 41). 

more correctly when he says : " To investigate the essence 
of a natural phenomenon, three conditions are necessary: 
We must first study and know the phenomenon itself, 
from all sides ; we must then determine in what relation 
it stands to other natural phenomena ; and lastly, when 
we have ascertained all these relations, we have to solve 
the problem of measuring these relations and the laws of 
mutual dependence — that is, of expressing them in num- 
bers. In the first period of chemistry, all the powers 
of men's minds were devoted to acquiring a knowledge of 
the properties of bodies; it was necessary to discover, 
observe, and ascertain their peculiarities. This is the 
alchemistical period. The second period embraces the 
determination of the mutual relations or connections of 
these properties ; this is the period of phlogistic chemistry. 
In the third period, in which we now are, we ascertain by 
weight and measure and express in numbers the degree 
in which the properties of bodies are mutually dependent. 
The inductive sciences begin with the substance itself, 
then come just ideas, and lastly, mathematics are called 
in, and, with the aid of numbers, complete the work." ^ 

As Galileo, Huygens, and JSTewton, by a series of bril- 
liant investigations and theories, such as those of the pen- 
dulum, the fall of bodies, finally of universal gravitation, 
established the usefulness of the mathematical treatment 
of physical phenomena, so Lavoisier and his school proved 
the correctness and usefulness of their views by the new 5. 

Tlieory of 

theory of combustion, as consisting in the combination of combustion 
a special body or element called oxygen with other bodies 

^ * Familiar Letters on Chemistry,' translated by Blyth, 4th ed., London, 
1859, p. 60. 



or elements. A very large field of research — all on the 
lines pointed out by the new school — was opened out. But 
the age for a further application of mathematical reason- 
ing came much more slowly in chemistry than in physical 

The latter had at least one great department, in which 
a small number of factors, all admitting of mathematical 
accuracy — those of distance, mass, and motion — sufficed 
to explain the phenomena, at least if viewed from a great 
distance. This science is the physics of the heavens, the 
science of cosmic phenomena. On this earth — in physical 
and still more in chemical phenomena — the matter stood 
very differently. Here we have not to deal with a few- 
measurable quantities only. A large number of elements 
or factors, of which only very few can be accurately 
measured, combine to make up what we called in the last 
chapter molar and molecular phenomena. In the study 
of inanimate nature, astronomy — the mechanics of the 
heavens — deals with the ^simplest relations ; chemistry — 
the science of the changes which bodies undergo when 
being combined or separated — deals with the most com- 
plicated side of reality. Physics occupy an intermediate 
position, and thus we can also trace in the history of 
physical research the twofold influence of the astronomical 
method of inquiry on one side, and the chemical on the 

But the general rule, that in chemical changes the 
weight of all the constituents put together never changes, 
was not the only numerical relation which came to the 
aid of students of nature, when they, at the end of the last 
century, betook themselves to exact measurements and 



determinations. That rule is indeed the foundation of all 
work in the laboratory, the principle which decides the 
degree of accuracy attained in every analysis, and which 
not infrequently is the only method of determining the 
presence of some undiscovered constituent.^ Not long 

^ The revolution in chemistry at 
the end of the last century manifests 
itself in nothing more than in the 
various distinct problems, corre- 
sponding to different courses of 
scientific thought and different in- 
terests, which have guided chemical 
research since that time. The first 
definite object was the search after 
the real elements, the attempt to 
decompose the existing substances 
of nature into their ultimate con- 
stituents. This interesting occu- 
pation somewhat pushed into the 
background the theoretical investi- 
gations regarding the forms of the 
combinations of the various ele- 
ments into compounds, still more 
the study of chemical affinity. A 
second definite object was the de- 
velopment of the theory of combus- 
tion which Lavoisier propounded, 
and the confirmation or refutation 
of the idea according to which 
oxygen occupied almost as import- 
ant a position in chemical reactions 
as phlogiston had done before. A 
third definiteobject was the develop- 
ment of analytical chemistry, the 
systematic and methodical use of 
the balance. So far as the first 
branch of this pursuit was con- 
cerned, Lavoisier's catalogue of the 
elements was still very incomplete ; 
it contained thirty-three members, 
including light and heat, and 
twenty-three of the substances 
which now figure in the list of the 
seventy elements enumerated in the 
text- books ; the alkalies and earths 
were still considered to be simple 
bodies. A great addition to our 
knowledge in this department came 

through Davy's decomposition of 
soda and potash. And after his 
proof of the elementary nature of 
chlorine the oxygen theory of La- 
voisier had also to be greatly modi- 
fied. '* Through a series of most 
important investigations, he rose in 
the beginning of this century to 
such eminence, that he was then 
considered to be the first represen- 
tative of chemical science. With 
great experimental ability he com- 
bined a singular freedom from all 
the theoretical doctrines which were 
recognised in his age " (Kopp, * Ent- 
wickelung der Chemie,' p. 451). In 
this he resembled Dalton and Fara- 
day and other natural philosophers 
in this country, on whom theoretical 
notions formed in the Continental 
schools had little or no influence. 
Qualitative analysis was less indebt- 
ed to Lavoisier than other branches 
of the science were. In fact, it was 
more at home in Sweden and Ger- 
many, where the interests of miner- 
alogy and metallurgy promoted it. 
Bergmann and Scheele in Sweden, 
Klaproth in Berlin, were the fore- 
runners of Berzelius and of the 
Berlin school of analysts. In this 
country Black and especially Caven- 
dish had carried out some important 
quantitative determinations, the ac- 
curacy of which seems very far be- 
hind modern standards (see Kopp, 
'Geschichte der Chemie,' vol. ii. p. 
70, &c., 1844). It was the introduc- 
tion of the notion of chemical equi- 
valence, a term used already by 
Cavendish, which furnished the 
ultimate test for accuracy and re- 
volutionised quantitative analysis. 







6. before the age of Lavoisier, another general conception 
proportions, had been introduced into chemical research ; this was the 
rule of definite proportions — i.e., the fact that substances, 
whether simple or compound, combine only in definite 
proportions of their weight, and that the numbers marking 
these proportions are characteristic of every definite 
chemical substance. It took some time, nearly a century, 
before this idea, which arose through the examination of 
neutral salts and the determination of the quantities of 
acids and alkalies which were wanted to effect mutual 
saturation, became clear ; before the rule of definite pro- 
portions was generally established, becoming a guide for 
chemical analysis. It is interesting to note how the 
vaguer terms of chemical affinity and elective attraction, 
of chemical action, of adhesion and elasticity — mostly 
borrowed from other departments of science where they 
had definite meanings — gradually disappeared, when by 
the aid of the chemical balance each simple substance 
and each definite compound began to be characterised, 
and labelled with a fixed number. Nevertheless, even at 
the beginning of this century, eminent chemists were still 
so much engaged in discussing the rival claims of the old 
phlogistic, and the modern theory of combustion, of Ber- 
thollet's cljemical equilibrium, of the so-called dynamical 
and the electro-chemical views of phenomena, that the first 
methodical attempt actually to fix these numbers — i.e., to 
give a table of chemical equivalents — remained unnoticed.^ 

^ The history of chemistry early j doctrine of chemical affinities, was 

in this century furnishes a good ex- evidently much influenced by the 

ample of the sway which theoretical i mathematical theory of attraction, 

views exercised over the minds of in- and by the mechanical laws of equi- 

vestigators. Berthollet, who began librium, which formed so prominent 

by critically examining Bergmann's a subject of investigation in the 

The merit of having made this attempt belongs to one 
who approached chemistry entirely from the mathematical 
side, who wrote the first chemical book with a title point- 
ing directly to measurements, but who perhaps spoilt his 
work by giving way to the fascination which regular 
numerical and geometrical arrangements have again and 
again exercised over philosophical inquirers. Jeremias 7. 
Benjamin Eichter — a name possessed of no popular cele- Richter. 
brity — published in 1792 to 1794, in three parts, his 
" Stoechiometry, or the art of measuring chemical ele- 
ments." ^ From his data, Fischer calculated in 1802 the 

writings of Laplace and his school. 
Chemical affinity was to be co- 
ordinated with what he called astro- 
nomical attraction ; both were to 
be ultimately the same physical 
property; they acted difierently, 
because in the case of gravitation 
the dimensions were so large, that 
the form, distances, and peculiar 
properties of the molecules had no 
influence. It was an attempt to 
introduce the astronomical vi.^w of 
matter into molecular physics, and 
to base chemistry upon this view. 
Berthollet adhered to the corpus- 
cular theory of heat against Rum- 
ford, who had just propounded his 
opinion that heat is not a consti- 
tuent part of bodies ; and he main- 
tained that chemical affinity was a 
function of the mass of bodies as 
was astronomical attraction. The 
germ of truth in Berthollet's views, 
which were approved by Laplace, 
but cast into oblivion under the 
influence of Proust and Richter's 
theory of fixed proportions, has 
in recent times been shown by 
Lothar Meyer (* Modem Theories of 
Chemistry,' Introduction), and by 
Ostwald ('Allgemeine Chemie,' vol. 
ii. p. 557, 1st ed., also ' Die Energie 
und ihre Wandlungen,' Leipzig, 

1888, p. 20). If the astronomical 
view of molecular phenomena pre- 
vented Berthollet from accepting 
Proust'sdoctrine of fixed proportions 
and definite combinations, Richter 
injured his own reputation by ad- 
hering to the nomenclature of the 
phlogiston theory after it had been 
discarded by French chemists, and 
in Germany after Klaproth's deter- 
minations in 1792. The oxygen 
theory of combustion of Lavoisier 
got such a firm hold on the minds 
of Continental chemists that the 
labours of those who, like Cavendish 
in England and Richter in Germany, 
put forward important discoveries 
in the language and on the principles 
of the older theory, were temporarily 
forgotten. See Kopp, * Entwickel- 
ung der Chemie,' p. 271, &c. 

^ Stoechiometry comes from the 
Greek to. a-Toixe^a, the constituent 
parts, and fxtrpuv, to measure. 
All Richter's works are connected 
with the application of mathematics 
to chemistry ; his inaugural disser- 
tation, which appeared in 1789, 
bearing the title ' de usu matheseos 
in chymia' (Kopp, 'Geschichte der 
Chemie,' vol. ii. p. 350). " Richter 
etait pr^occup^ de I'idee d'applitjuer 
les math^matiques a la chimie, et en 






first table of chemical equivalents, taking sulphuric acid 
as the standard with the figure 1000. 

The conviction that chemical substances combine ac- 
cording to fixed and simple proportions gained ground 
on the Continent, chiefly during the discussion in which 
Proust finally disproved and defeated Berthollet's theory 
of chemical affinity ; but it is to Dalton that the doctrine 
of fixed and multiple proportions is indebted for a con- 
sistent exposition. Dalton based it upon a mental re- 
presentation which ever since has been the soul of all 
chemical reasoning. 

When I^ewton, from the measurable data of the move- 
ments of cosmic bodies, deduced the celebrated gravita- 
tion formula, he had to descend to molar — nay, even to 
molecular — dimensions, and to express it as a relation 
referring to the very elements of matter, before he could 
apply it in a useful manner : he had to express it as a 
formula which had reference to the smallest portions of 
matter. In the same way, the measurements made by 

particulier de decouvrir des relations 
numeriques entre lea quantitds des 
corps qui se combinent. Ses efforts, 
dans cette direction, n'ont pas et^ 
egalement heureux ; car, s'il a re- 
connu et dnonc^ le premier la loi de 
proportionnalit^ entre les quantitea 
de bases qui s'unissent au meme 
poids d'acide et entre les quantites 
d'acides qui s'unissent au meme 
poids de base, fait important et ex- 
act, il a cherche k d^montrer, d'un 
autre cot^, que ces quantites fermai- 
ent des series numeriques dout les 
termes augmentent suivant des re- 
lations simples, ce qui est errone. 
. . . Ces erreurs n'ont pas echappd, 
sans doute, h. I'attention des con- 
temporains de Richter et ont con- 
tribue h, discrediter ses travaux. 

. . . Mais nous n'avons pas a insister 
sur ce dernier point. Relevons, 
dans Toeuvre de Richter, les idees 
justes et les decouvertes fondamen- 
tales qui recommandent d'autant 
plus son nom a I'attention recon- 
naissante de la posterite qu'il est 
demeur^ meconnu et presque ignor^ 
de son temps " (Wurtz, * La Thdorie 
atomique," /'"^ ed., 1893, p. 9, &c.) 
" L'opposition meme, qu'il profes- 
sait pour les doctrines du reforma- 
teur [Lavoisier] semble avoir con- 
tribue b, discrediter les travaux de 
Richter : son heure n'etait pas 
venue ; I'int^ret ^tait ailleurs, et 
en AUemagne, comme en Fra